Дисертації з теми "Codes minimaux"
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1
Qian, Liqin. "Contributions to the theory of algebraic coding on finite fields and rings and their applications." Electronic Thesis or Diss., Paris 8, 2022. http://www.theses.fr/2022PA080064.
Анотація:
La théorie du codage algébrique sur les corps et les anneaux finis a une grande importance dans la théorie de l'information en raison de leurs diverses applications dans les schémas de partage de secrets, les graphes fortement réguliers, les codes d'authentification et de communication. Cette thèse aborde plusieurs sujets de recherche selon les orientations dans ce contexte, dont les méthodes de construction sont au cœur de nos préoccupations. Plus précisément, nous nous intéressons aux constructions de codes optimaux (ou codes asymptotiquement optimaux), aux constructions de codes linéaires à "hull" unidimensionnelle, aux constructions de codes minimaux et aux constructions de codes linéaires projectifs. Les principales contributions sont résumé comme suit. Cette thèse fournie une description explicite des caractères additifs et multiplicatifs sur les anneaux finis (précisément S\mathbb{F}_q+u\mathbb{F}_q~(u^2= 0)S et _\mathbb{F} _q +u\mathbb{F}_q~(u^2=u)s), utilise des sommes Gaussiennes, hyper Eisenstein et Jacobi et fournit plusieurs classes de nouveaux codes optimaux (ou asymptotiquement optimaux) avec des paramètres flexibles, propose des codes linéaires (optimaux ou quasi-optimal) avec une "hull" unidimensionnelle sur des corps finis en utilisant des outils de la théorie de la somme Gaussienne. De plus, cette thèse explore plusieurs classes de codes linéaires binaires (optimaux pour la borne de Griesmer bien connue) sur des corps finis basés sur deux constructions génériques utilisant des fonctions. Aussi, elle détermine leurs paramètres et leurs distributions de poids et en déduit plusieurs familles infinies de codes linéaires minimaux. Enfin, elle étudie des constructions optimales de plusieurs classes de codes linéaires binaires projectifs avec peu de poids et leurs codes duaux correspondantsAlgebraic coding theory over finite fields and rings has always been an important research topic in information theory thanks to their various applications in secret sharing schemes, strongly regular graphs, authentication and communication codes.This thesis addresses several research topics according to the orientations in this context, whose construction methods are at the heart of our concerns. Specifically, we are interested in the constructions of optimal codebooks (or asymptotically optimal codebooks), the constructions of linear codes with a one-dimensional hull, the constructions of minimal codes, and the constructions of projective linear codes. The main contributions are summarized as follows. This thesis gives an explicit description of additive and multiplicative characters on finite rings (precisely _\mathbb{F}_q+u\mathbb{F}_q~(u^2= 0)s and S\mathbb{F}_q+u\mathbb{F}_q~(u^2=u)S), employees Gaussian, hyper Eisenstein and Jacobi sums and proposes several classes of optimal (or asymptotically optimal) new codebooks with flexible parameters. Next, it proposes(optimal or nearly optimal) linear codes with a one-dimensional hull over finite fields by employing tools from the theory of Gaussian sums. It develops an original method to construct these codes. It presents sufficient conditions for one-dimensional hull codes and a lower bound on its minimum distance. Besides, this thesis explores several classes of (optimal for the well-known Griesmer bound) binary linear codes over finite fields based on two generic constructions using functions. It determines their parameters and weight distributions and derives several infinite families of minimal linear codes. Finally, it studies (optimal for the sphere packing bound) constructions of several classes of projective binary linear codes with a few weight and their corresponding duals codes
2
Luu, Tien Duc. "Régularité des cônes et d’ensembles minimaux de dimension 3 dans R4." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112301/document.
Анотація:
On étudie dans cette thèse la régularité des cônes et d'ensembles de dimension 3 dans l'espace Euclidien de dimension 4.Dans la première partie, on étudie d'abord la régularité Bi-Hölderienne des cônes minimaux de dimension 3 dans l'espace Euclidien de dimension 4. Ceci nous permet ensuite de montrer qu'il existe un difféomorphisme locale entre un cône minimal de dimension 3 dans l'espace Euclidien de dimension 4 et un cône minimal de dimension 3, de type P, Y ou T, loin d'origine. La méthode est la même que pour les ensembles minimaux de dimension 2. On construit des compétiteurs et on se ramène aux situations connues des ensembles minimaux de dimension 2 dans l'espace Euclidien de dimension 3.Dans la deuxième partie, on utilise le résultat de la première partie pour donner quelques résultats de régularité Bi-Hölderienne pour les ensembles minimaux de dimension 3 dans l'espace Euclidien de dimension 4. On s'intéresse aussi aux ensembles minimaux de Mumford-Shah et on obtient un résultat de l'existence d'un point de type TIn this thesis we study the problems of regularity of three-dimensional minimal cones and sets in l'espace Euclidien de dimension 4In the first part we study the Hölder regularity for minimal cones of dimension 3 in l'espace Euclidien de dimension 4. Then we use this for showing that there exists a local diffeomorphic mapping between a minimal cone of dimension 3 and a minimal cone of dimension 3 of type P, Y or T, away from the origin. The techniques used here are the same as the ones for the regularity of two-dimensional minimal sets. We construct some competitors to reduce to the known situation of two-dimensional minimal sets in l'espace Euclidien de dimension 3.In the second part, we use the first part to give somme results of the Hölder regularity for three-dimensional minimal sets in l'espace Euclidien de dimension 4. We interested also in Mumford-Shah minimal sets and we get a result of the existence of a T-point
3
Miller, John. "High code rate, low-density parity-check codes with guaranteed minimum distance and stopping weight /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2003. http://wwwlib.umi.com/cr/ucsd/fullcit?p3090443.
4
Fang, Yangqin. "Minimal sets, existence and regularity." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112191/document.
Анотація:
Cette thèse s’intéresse principalement à l’existence et à la régularité desensembles minimaux. On commence par montrer, dans le chapitre 3, que le problème de Plateau étudié par Reifenberg admet au moins une solution. C’est-à-dire que, si l’onse donne un ensemble compact B⊂R^n et un sous-groupe L du groupe d’homologie de Čech H_(d-1) (B;G) de dimension (d-1) sur un groupe abelien G, on montre qu’il existe un ensemble compact E⊃B tel que L est contenu dans le noyau de l’homomorphisme H_(d-1) (B;G)→H_(d-1) (E;G) induit par l’application d’inclusion B→E, et pour lequel la mesure de Hausdorff H^d (E∖B) est minimale (sous ces contraintes). Ensuite, on montre au chapitre 4, que pour tout ensemble presque minimal glissant E de dimension 2, dans un domaine régulier Σ ressemblant localement à un demi espace, associé à la frontière glissante ∂Σ, et tel que E⊃∂Σ, il se trouve qu’à la frontière E est localement équivalent, par un homéomorphisme biHöldérien qui préserve la frontière, à un cône minimal glissant contenu dans un demi plan Ω, avec frontière glissante ∂Ω. De plus les seuls cônes minimaux possibles dans ce cas sont ∂Ω seul, ou son union avec un cône de type P_+ ou Y_+This thesis focuses on the existence and regularity of minimal sets. First we show, in Chapter 3, that there exists (at least) a minimizerfor Reifenberg Plateau problems. That is, Given a compact set B⊂R^n, and a subgroup L of the Čech homology group H_(d-1) (B;G) of dimension (d-1)over an abelian group G, we will show that there exists a compact set E⊃B such that L is contained in the kernel of the homomorphism H_(d-1) (B;G)→H_(d-1) (E;G) induced by the natural inclusion map B→E, and such that the Hausdorff measure H^d (E∖B) is minimal under these constraints. Next we will show, in Chapter 4, that if E is a sliding almost minimal set of dimension 2, in a smooth domain Σ that looks locally like a half space, and with sliding boundary , and if in addition E⊃∂Σ, then, near every point of the boundary ∂Σ, E is locally biHölder equivalent to a sliding minimal cone (in a half space Ω, and with sliding boundary ∂Ω). In addition the only possible sliding minimal cones in this case are ∂Ω or the union of ∂Ω with a cone of type P_+ or Y_+
5
Ketkar, Avanti Ulhas. "Code constructions and code families for nonbinary quantum stabilizer code." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/2743.
Анотація:
Stabilizer codes form a special class of quantum error correcting codes. Nonbinary quantum stabilizer codes are studied in this thesis. A lot of work on binary quantum stabilizer codes has been done. Nonbinary stabilizer codes have received much less attention. Various results on binary stabilizer codes such as various code families and general code constructions are generalized to the nonbinary case in this thesis. The lower bound on the minimum distance of a code is nothing but the minimum distance of the currently best known code. The focus of this research is to improve the lower bounds on this minimum distance. To achieve this goal, various existing quantum codes are studied that have good minimum distance. Some new families of nonbinary stabilizer codes such as quantum BCH codes are constructed. Different ways of constructing new codes from the existing ones are also found. All these constructions together help improve the lower bounds.
6
Zeng, Fanxuan. "Nonlinear codes: representation, constructions, minimum distance computation and decoding." Doctoral thesis, Universitat Autònoma de Barcelona, 2014. http://hdl.handle.net/10803/284241.
Анотація:
Resum
La teoria de codis estudia el disseny de codis correctors d'errors per a la transmisió fidedigne d'informació per un canal amb soroll. Un codi corrector d'errors (o simplement codi) es un proces que consisteix en expressar una seqüència d'elements sobre un alfabet de tal manera que qualsevol error que sigui introduït pot ser detactat i corregit (amb limitacions), i està basat en la tècnica d'afegir elements redundants. Aquest proces inclou la codifcació, la transmisió i la descodifcació de la seqüència d'elements. La majoria dels codis utilitzat són codis bloc i la majoria d'ells tenen una estructura lineal, que facilita el procés de codifcació i descodifcació.
En aquesta memòria, estudiarem codis correctors d'errors no lineals. Mal¬grat els codis no lineals no tenen les mateixes bones propietats per codifcar i descodifcar com els lineals, el codis no lineals tenen interes ates que alguns dels millors codis no son lineals.
La primera qüestió que apareix quan s'utilitzen codis no lineals és la seva representació. Els codis lineals poden ser representats utilitzant una matriu generadora o una matriu de control. La millor manera de representar un codi no lineal és utilitzar la representacio kernel/caset, que permet represen¬tar un codi mitjan
7
Cadic, Emmanuel. "Construction de Turbo Codes courts possédant de bonnes propriétés de distance minimale." Limoges, 2003. http://aurore.unilim.fr/theses/nxfile/default/2c131fa5-a15a-4726-8d49-663621bd2daf/blobholder:0/2003LIMO0018.pdf.
Анотація:
L'objectif de cette thèse est de réaliser des turbo codes possédant de bonnes distances minimales et de contribuer ainsi à repousser le phénomène ``d'error floor'' qui correspond à un seuil de l'ordre de 10-6 pour le taux d'erreur résiduelles binaires en dessous duquel la pente de la courbe de TEB diminue de façon significative. Ce problème s'est sensiblement amélioré avec l'apparition des codes duo-binaires de Berrou [11] qui permettent notamment d'obtenir de meilleures distances minimales. Pour obtenir de bonnes distances minimales avec des turbo codes courts (longueur inférieure à 512), la construction initialement utilisée et étudiée dans cette thèse a été celle proposée par Carlach et Vervoux [26] qui permet d'obtenir d'excellentes distances minimales mais qui malheureusement s'avère moins performante en terme de décodage notamment pour des raisons propres à la structure. Après avoir identifié les raisons qui empêchent un décodage efficace de cette famille de codes, nous faisons évoluer ces codes en utilisant des structures graphiques différentes reposant toujours sur l'assemblage de codes composants de petite complexité. L'idée est de réaliser ce changement sans pour autant perdre les qualités de distance minimale de ces codes et par conséquent il est nécessaire de comprendre pourquoi les distances minimales de cette famille initiale de codes sont bonnes et de définir un critère de choix pour les codes composants. Le critère de choix ne dépend pas de la distance minimale des codes composants mais du polynôme de transition de ces codes et permet donc de sélectionner des codes composants de très faible complexité qui sont assemblés de façon à générer des treillis cycliques à seulement 4 états. Ces treillis sont alors utilisés pour élaborer des turbo codes parallèle ou série présentant de bonnes distances minimales. Certains codes auto-duaux extrémaux sont notamment construits ainsiThis thesis is aimed at building turbo codes with good minimum distances and delaying the``error-floor'' which corespond to a threshold of 10-6 for the binary error rate. Under this threshold, the slope of the curve decreases significantly. This problem is alleviated by the use of duo-binary turbo codes [11] which guarantee better minimum distances. In order to obtain good minimum distances with short turbo codes (length inferior to 512), the first construction used and studied is the one proposed by Carlach and Vervoux [26]. It allows to obtain very good minimum distances but its decoding is unfortunately very difficult because of its structure. After identifying the reasons for this problem, we have modified these codes by using some graphicals structures which are the gathering of low complexity components codes. The idea is to realize this change without loosing the minimum distances properties, and consequently we had to understand why minimum distances are good for this familly of codes and define a new criteria to choose ``good'' components codes. This criteria is independent from the minimum distance of the component codes because it is derived from the Input-Output Weight Enumerator (IOWE) of the components codes. It allows us to choose components codes with very low complexity which are combined in order to provide 4-state tail-biting trellises. These trellises are then used to build multiple parallel concatenated and serial turbo codes with good minimum distances. Some extremal self-dual codes have been built in that way
8
Siap, Irfan. "Generalized [Gamma]-fold weight enumerators for linear codes and new linear codes with improved minimum distances /." The Ohio State University, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488193272067477.
9
Kumar, Santosh. "Upper bounds on minimum distance of nonbinary quantum stabilizer codes." Thesis, Texas A&M University, 2004. http://hdl.handle.net/1969.1/2744.
Анотація:
The most popular class of quantum error correcting codes is stabilizer codes. Binary quantum stabilizer codes have been well studied, and Calderbank, Rains, Shor and Sloane (July 1998) have constructed a table of upper bounds on the minimum distance of these codes using linear programming methods. However, not much is known in the case of nonbinary stabilizer codes. In this thesis, we establish a bridge between selforthogonal classical codes over the finite field containing q2 elements and quantum codes, extending and unifying previous work by Matsumoto and Uyematsu (2000), Ashikhmin and Knill (November 2001), Kim and Walker (2004). We construct a table of upper bounds on the minimum distance of the stabilizer codes using linear programming methods that are tighter than currently known bounds. Finally, we derive code construction techniques that will help us find new codes from existing ones. All these results help us to gain a better understanding of the theory of nonbinary stabilizer codes.
10
Chan, Evelyn Yu-San. "Heuristic optimisation for the minimum distance problem." Thesis, Nottingham Trent University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.324569.
11
Ahmed, Naveed, and Waqas Ahmed. "Classification of perfect codes and minimal distances in the Lee metric." Thesis, Linnaeus University, School of Computer Science, Physics and Mathematics, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-6574.
Анотація:
Perfect codes and minimal distance of a code have great importance in the study of theoryof codes. The perfect codes are classified generally and in particular for the Lee metric.However, there are very few perfect codes in the Lee metric. The Lee metric hasnice properties because of its definition over the ring of integers residue modulo q. It isconjectured that there are no perfect codes in this metric for q > 3, where q is a primenumber.The minimal distance comes into play when it comes to detection and correction oferror patterns in a code. A few bounds on the number of codewords and minimal distanceof a code are discussed. Some examples for the codes are constructed and their minimaldistance is calculated. The bounds are illustrated with the help of the results obtained.
12
Cavallotto, Edoardo. "Résultats de régularité et d'existence pour des ensembles minimaux ; Problème de Plateau." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLS180/document.
Анотація:
Résoudre le Problème de Plateau signifie trouver la surface ayant l’aire minimale parmi toutes les surfaces avec un bord donné.Une partie du problème réside dans le fait de donner des définitions appropriées aux concepts de “surface”, “aire” et “bord”. Dans notre contexte les objets considérés sont ensembles dont la mesure de Hausdorff est localement finie. La condition de bord glissant est donnée par rapport à une famille à un paramètre de déformations compactes laquelle permet au bord de glisser le long d'un ensemble fermé. La fonctionnelle à minimiser est liée aux problèmes de capillarité et de frontière libre.On s'est intéressé aux cônes minimaux glissants, c'est à dire les cônes tangents aux surfaces minimaux glissantes dans des points sur son bord. En particulier on a étudié les cônes contenus dans un demi-espace dont le bord peut glisser le long l'hyperplane bornant le demi-espace. Après avoir donné une classification des cônes minimaux de dimension un dans le demi-plan on a présenté quatre nouveau cône minimaux de dimension deux dans le demi-espace (lesquels ne peuvent pas être obtenus comme un produit cartésien d'un des cône précédents avec la droite réelle). La technique utilisé c'est les calibrations couplées, qui dans un cas on a pu généraliser en grands dimensions.Afin de montrer que la liste des cônes minimaux est complète on a entamé la classification des cônes qui satisfont les conditions nécessaires pour la minimalité, pour lesquels on a obtenu des meilleurs compétiteurs à l'aide des simulations numériquesSolving the Plateau problem means to find the surface with minimal area among all surfaces with a given boundary. Part of the problem actually consists of giving a suitable definition to the notions of “surface”, “area” and “boundary”. In our setting the considered objects are sets whose Hausdorff area is locally finite. The sliding boundary condition is given in term of a one parameter family of compact deformations which allows the boundary of the surface to moove along a closed set. The area functional is related to capillarity and free-boundary problems, and is a slight modification of the Hausdorff area.We focused on minimal boundary cones ; that is to say tangent cones on boundary points of sliding minimal surfaces. In particular we studied cones contained in an half-space and whose boundary can slide along the bounding hyperplane. After giving a classification of one-dimensional minimal cones in the half-plane we provided four new two-dimensional minimal cones in the three-dimensional half space (which cannot be obtained as the Cartesian product of the real line with one of the previous cones). We employed the technique of paired calibrations and in one case could also generalise it to higher dimension.In order to prove that the provided list of minimal cones is complete, we started the classification of cones satisfying the necessary conditions for the minimality, and with numeric simulations we obtained better competitors for these new candidates
13
Wunderlich, Marcel [Verfasser], and Boris [Akademischer Betreuer] Vertman. "Mean curvature flow of cones near minimal cones / Marcel Wunderlich ; Betreuer: Boris Vertman." Münster : Universitäts- und Landesbibliothek Münster, 2019. http://d-nb.info/1190175517/34.
14
Papadimitriou, Panayiotis D. "Code design based on metric-spectrum and applications." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1365.
Анотація:
We introduced nested search methods to design (n, k) block codes for arbitrary channels by optimizing an appropriate metric spectrum in each iteration. For a given k, the methods start with a good high rate code, say k/(k + 1), and successively design lower rate codes up to rate k/2^k corresponding to a Hadamard code. Using a full search for small binary codes we found that optimal or near-optimal codes of increasing length can be obtained in a nested manner by utilizing Hadamard matrix columns. The codes can be linear if the Hadamard matrix is linear and non-linear otherwise. The design methodology was extended to the generic complex codes by utilizing columns of newly derived or existing unitary codes. The inherent nested nature of the codes make them ideal for progressive transmission.
Extensive comparisons to metric bounds and to previously designed codes show the optimality or near-optimality of the new codes, designed for the fading and the additive white Gaussian noise channel (AWGN). It was also shown that linear codes can be optimal or at least meeting the metric bounds; one example is the systematic pilot-based code of rate k/(k + 1) which was proved to meet the lower bound on the maximum cross-correlation. Further, the method was generalized such that good codes for arbitrary channels can be designed given the corresponding metric or the pairwise error probability.
In synchronous multiple-access schemes it is common to use unitary block codes to transmit the multiple users information, especially in the downlink. In this work we suggest the use of newly designed non-unitary block codes, resulting in increased throughput efficiency, while the performance is shown not to be substantially sacrificed. The non-unitary codes are again developed through suitable nested searches. In addition, new multiple-access codes are introduced that optimize certain criteria, such as the sum-rate capacity.
Finally, the introduction of the asymptotically optimum convolutional codes for a given constraint length, reduces dramatically the search size for good convolutional codes of a certain asymptotic performance, and the consequences to coded code-division multiple access (CDMA) system design are highlighted.
15
Bazzi, Louay Mohamad Jamil 1974. "Minimum distance of error correcting codes versus encoding complexity, symmetry, and pseudorandomness." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/17042.
Анотація:
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (leaves 207-214).
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
We study the minimum distance of binary error correcting codes from the following perspectives: * The problem of deriving bounds on the minimum distance of a code given constraints on the computational complexity of its encoder. * The minimum distance of linear codes that are symmetric in the sense of being invariant under the action of a group on the bits of the codewords. * The derandomization capabilities of probability measures on the Hamming cube based on binary linear codes with good distance properties, and their variations. Highlights of our results include: * A general theorem that asserts that if the encoder uses linear time and sub-linear memory in the general binary branching program model, then the minimum distance of the code cannot grow linearly with the block length when the rate is nonvanishing. * New upper bounds on the minimum distance of various types of Turbo-like codes. * The first ensemble of asymptotically good Turbo like codes. We prove that depth-three serially concatenated Turbo codes can be asymptotically good. * The first ensemble of asymptotically good codes that are ideals in the group algebra of a group. We argue that, for infinitely many block lengths, a random ideal in the group algebra of the dihedral group is an asymptotically good rate half code with a high probability. * An explicit rate-half code whose codewords are in one-to-one correspondence with special hyperelliptic curves over a finite field of prime order where the number of zeros of a codeword corresponds to the number of rational points.
(cont.) * A sharp O(k-1/2) upper bound on the probability that a random binary string generated according to a k-wise independent probability measure has any given weight. * An assertion saying that any sufficiently log-wise independent probability measure looks random to all polynomially small read-once DNF formulas. * An elaborate study of the problem of derandomizability of AC₀ by any sufficiently polylog-wise independent probability measure. * An elaborate study of the problem of approximability of high-degree parity functions on binary linear codes by low-degree polynomials with coefficients in fields of odd characteristics.
by Louay M.J. Bazzi.
Ph.D.
16
Fingeret, Samuel (Samuel P. ). "Defeating code reuse attacks with minimal tagged architecture." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/105986.
Анотація:
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 93-97).
In this thesis, we argue that software-based defenses to code reuse attacks are fundamentally flawed. With code pointer integrity as a case study, we show that a secure and efficient software-based defense to code reuse attacks is impossible and thus motivate the case for hardware approaches. We then propose our tagged architecture system Taxi (Tagged C) as a practical defense against code reuse attacks which minimally modifies existing hardware components. We also propose strong defense policies which aim to guarantee security while minimizing tag memory usage. Our Taxi prototype, a modified RISC-V ISA simulator, demonstrates that we can defeat code reuse attacks with high compatibility and low memory overhead.
by Samuel Fingeret.
M. Eng.
17
Nikolaidis, Christos. "On binary linear codes with 2-transitive automorphism group and minimum weight four." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318832.
18
Martin, Timothy Michael. "Codes of Interaction." VCU Scholars Compass, 2005. http://scholarscompass.vcu.edu/etd/849.
Анотація:
The ideas within this thesis are meant to clarify my explorations, research and painting practice during my studies at Virginia Commonwealth University. I expand on my general statements about being fascinated by advancing technologies and concerned about the after effects of these advancements. The writing explores my curiosity about the internal, skeletal structure of things and how they operate. I explain how the paintings are idiosyncratic hybrids that evoke animation, imaginary scientific propositions, blueprints, maps, and advancing technologies. The work combines these interests with my observations of day-to-day experiences. Isolated events provide found compositions which I then manipulate: a seemingly mundane bike ride gets mapped into a well–ordered schematic of social interaction.
19
Appleby, Paul [Verfasser]. "Mean curvature flow of surfaces asymptotic to minimal cones / Paul Appleby." Berlin : Freie Universität Berlin, 2011. http://d-nb.info/1025510003/34.
20
Galand, Fabien. "Construction de codes Z indice p à la puissance k linéaires de bonne distance minimale et schémas de dissimulation fondés sur les codes de recouvrement." Caen, 2004. http://www.theses.fr/2004CAEN2047.
Анотація:
Cette thèse étudie deux axes de recherches reposant sur les codes. Chaque axe porte sur un paramètre particulier. Le premier axe est celui de la correction d'erreur, et nous nous intéressons à la distance minimale des codes. Notre objectif est de construire des codes sur Fp ayant une bonne distance minimale. Pour cela nous utilisons conjointement le relèvement de Hensel et la Zpk-linéarité. Nous donnons la distance minimale en petite longueur d'une généralisation des codes de Kerdock et de Preparata, ainsi que des relevés des codes de résidus quadratiques. Parmi ces codes, nous en obtenons quatre égalant les meilleurs codes linéaires. Nous donnons également une construction visant à augmenter le cardinal des codes Zpk-linéaires par ajout de translatés. Cette construction nous conduit à une borne supérieure sur le cardinaux des codes Zpk-linéaires. Le second axe, disjoint du premier dans son objectif, mais le rejoignant sur les objets étudiés, est la construction de schémas de dissimulation. Nous relions cette problématique, relevant de la stéganographie, à la construction de codes de recouvrement. Nous envisageons deux modàles de schémas. Ces modàles sont prouvés équivalents aux cette équivalence pour mettre à jour la structure des recouvrements utilisés dans les travaux déjà publiés. Cette équivalence nous sert également à déduire des bornes supérieures sur la capacité des schémas, et en donnant des constructions fondées sur les recouvrements linéaires nous obtenons des bornes inférieures.
21
Mahmudi, Ali. "The investigation into generic VHDL implementation of generalised minimum distance decoding for Reed Solomon codes." Thesis, University of Huddersfield, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.417302.
Анотація:
This thesis is concerned with the hardware implementation in VHDL (VHSIC Hardware Description Language) of a Generalised Minimum Distance (GMD) decoder for Reed Solomon (RS) codes. The generic GMD decoder has been implemented for the Reed Solomon codes over GF(28 ). It works for a number of RS codes: RS(255, 239), RS(255, 241), RS(255, 243), RS(255, 245), RS(255, 247), RS(255, 249), and RS(255, 251). As a comparison, a Hard Decision Decoder (HDD) using the Welch-Berlekamp algorithm for the same RS codes is also implemented. The designs were first implemented in MAT LAB. Then, the designs were written in VHDL and the target device was the AItera Field Programmable Gate Array (FPGA) Stratix EP 1 S25-B672C6. The GMD decoder achieved an internal clock speed of 66.29 MHz with RS(255, 251) down to 57.24 MHz with RS(255, 239). In the case of HDD, internal clock speeds were 112.01 MHz with RS(255, 251) down to 86.23 MHz with RS(255, 239). It is concluded that the GMD needs a lot of extra hardware compared to the HDD. The decoder GMD needs as little as 35% extra hardware in the case of RS(255, 251) decoder, but it needs 100% extra hardware for the RS(255, 241) decoder. If there is an option to choose the type of RS code to use, it is preferable to use the HDD decoder rather than the GMD decoder. In real world, the type of RS code to use is usually fixed by the standard regulation. Hence, one of the alternative way to enhance the decoding performance is by using the GMD decoder
22
Assuena, Samir. "Códigos metacíclicos." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-30102013-065155/.
Анотація:
Neste trabalho, consideramos álgebras de grupo semissimples F_G de grupos metacíclicos não abelianos que cindem sobre corpos finitos. Inicialmente, damos condições para que o número de componentes simples da álgebra F_G seja minimal e encontramos os idempotentes centrais primitivos quando a ordem do grupo é igual a p^l^, onde p e l são números primos distintos. Posteriormente, obtemos condições necessárias e suficientes para que o número de componentes simples da álgebra F_G seja minimal no caso em que a ordem do grupo é igual a 2n. Finalmente, quando G=D_{p^}, o grupo diedral de ordem 2p^, obtemos duas decomposições da álgebra F_D_{p^}$ como soma direta de ideais à esquerda minimais, calculamos suas dimensões e pesos e mostramos que, em uma destas decomposições, os códigos à esquerda minimais não são equivalentes a códigos abelianos, dando uma resposta afirmativa para uma conjectura formulada por Sabin e Lomonaco em 1995.We consider semisimple group algebras F_G of non abelian split metacyclic groups over a finite field. First we give necessary and suficiente conditions for them to have a minimal number of simple components and find the primitive central idempotents of F_G in the case when the order G is equals p^l^, where p and l are different prime numbers. Then, we consider the special case when the order of G is 2n. Finally, when G=D_{p^} the dihedral group of order 2p^, we obtain two decomposition of the algebra into direct sum of minimal left ideals, compute their dimensions and weights. We show that one of these decompositions gives raise to minimal codes that are not combinatorially equivalent to abelian codes giving an affirmative answer to a conjecture formulated by Sabin and Lomonaco in 1995.
23
Corazza, Federico Augusto. "Analysis of graph-based quantum error-correcting codes." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23801/.
Анотація:
With the advent of quantum computers, there has been a growing interest in the practicality of this device. Due to the delicate conditions that surround physical qubits, one could wonder whether any useful computation could be implemented on such devices. As we describe in this work, it is possible to exploit concepts from classical information theory and employ quantum error-correcting techniques. Thanks to the Threshold Theorem, if the error probability of physical qubits is below a given threshold, then the logical error probability corresponding to the encoded data qubit can be arbitrarily low. To this end, we describe decoherence which is the phenomenon that quantum bits are subject to and is the main source of errors in quantum memories. From the cause of error of a single qubit, we then introduce the error models that can be used to analyze quantum error-correcting codes as a whole. The main type of code that we studied comes from the family of topological codes and is called surface code. Of these codes, we consider both the toric and planar structures. We then introduce a variation of the standard planar surface code which better captures the symmetries of the code architecture. Once the main properties of surface codes have been discussed, we give an overview of the working principles of the algorithm used to decode this type of topological code: the minimum weight perfect matching. Finally, we show the performance of the surface codes that we introduced, comparing them based on their architecture and properties. These simulations have been performed with different error channel models to give a more thorough description of their performance in several situations showing relevant results.
24
Fang, Juing. "Décodage pondère des codes en blocs et quelques sujets sur la complexité du décodage." Paris, ENST, 1987. http://www.theses.fr/1987ENST0005.
Анотація:
Etude de la compléxité théorique du décodage des codes en blocs à travers une famille d'algorithmes basée sur le principe d'optimisation combinatoire. Puis on aborde un algorithme parallèle de décodage algébrique dont la complexitré est liée au niveau de bruit du canal. Enfin on introduit un algorithme de Viterbi pour les applications de traitement en chaînes.
25
Assis, Ailton Ribeiro de. "Idempotentes em Álgebras de Grupos e Códigos Abelianos Minimais." Universidade Federal da Paraíba, 2011. http://tede.biblioteca.ufpb.br:8080/handle/tede/7401.
Анотація:
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In this work, we study the semisimple group algebras FqCn of the finite abelian groups Cn over a finite field Fq and give conditions so that the number of its simple components is minimal; i.e. equal to the number of simple components of the rational group algebra of the same group. Under such conditions, we compute the set of primitive idempotents of FqCn and from there, we study the abelian codes as minimal ideals of the group algebra, which are generated by the primitive idempotents, computing their dimension and minimum distances.
Neste trabalho, estudamos álgebras de grupos semisimples FqCn de grupos abelianos finitos Cn sobre um corpo finito Fq e as condições para que o número de componentes simples seja mínimo, ou seja igual ao número de componentes simples sobre a álgebra de grupos racionais do mesmo grupo. Sob tais condições, calculamos o conjunto de idempotentes primitivos de FqG e a de partir daí, estudamos os códigos cíclicos como ideais minimais da álgebra de grupo, os quais são gerados pelos idempotentes primitivos, calculando suas dimensões e distâncias mínimas.
26
Augot, Daniel. "Étude algèbrique des mots de poids minimum des codes cycliques, méthodes d'algèbre linéaire sur les corps finis." Phd thesis, Université Pierre et Marie Curie - Paris VI, 1993. http://tel.archives-ouvertes.fr/tel-00723227.
Анотація:
Nous étudions les mots de poids minimal des codes correcteurs d'erreurs cycliques. Les fonctions symétriques élémentaires et les fonctions puissances des localisateurs de ces mots vérifient les identités de Newton. Dans le premier chapitre celles-ci sont étudiées comme un système d'équations algébriques, dont les solutions sont étudiées par transformation de Fourier. Dans le chapitre II, le lien est fait avec les codes correcteurs d'erreurs cycliques. Sur quelques exemples, il est montré comment étudier les mots de poids minimal sur la donnée d'une base standard de l'idéal engendré par les équations de Newton. Dans le chapitre III, les relations de Newton sont utilisées d'un point de vue théorique, et des résultats sur les mots de poids minimal de certains codes BCH sont obtenus. Ces calculs se placent dans le contexte de la théorie des corps finis. Dans le chapitre IV, un algorithme est développé pour calculer une base normale sur un corps fini. Un point de vue d'algèbre linéaire est choisi, et d'autres problèmes sont abordés (calcul du polynôme minimal, de la forme de Frobenius d'une matrice, lorsque la factorisation du polynôme caractéristique est connue).
27
Augot, Daniel. "Etude algebrique des mots de poids minimum des codes cycliques, methodes d'algebre lineaire sur les corps finis." Paris 6, 1993. https://tel.archives-ouvertes.fr/tel-00723227.
Анотація:
Nous etudions les mots de poids minimal des codes correcteurs d'erreurs cycliques. Les fonctions symetriques elementaires et les fonctions puissances des localisateurs de ces mots verifient les identites de newton. Dans le premier chapitre celles-ci sont etudiees comme un systeme d'equations algebriques, dont les solutions sont etudiees par transformation de fourier. Dans le chapitre ii, le lien est fait avec les codes correcteurs d'erreurs cycliques. Sur quelques exemples, il est montre comment etudier les mots de poids minimal sur la donnee d'une base standard de l'ideal engendre par les equations de newton. Dans le chapitre iii, les relations de newton sont utilisees d'un point de vue theorique, et des resultats sur les mots de poids minimal de certains codes bch sont obtenus. Ces calculs se placent dans le contexte de la theorie des corps finis. Dans le chapitre iv, un algorithme est developpe pour calculer une base normale sur un corps fini. Un point de vue d'algebre lineaire est choisi, et d'autres problemes sont abordes (calcul du polynome minimal, de la forme de frobenius d'une matrice, lorsque la factorisation du polynome caracteristique est connue)
28
Al-Fahad, Jasem Y. "Reform of building codes, regulations, administration and enforcement in Kuwait : within the legal, administrative, technical & social framework." Thesis, Loughborough University, 2012. https://dspace.lboro.ac.uk/2134/9883.
Анотація:
The majority of building code development and implementation practices are normally connected with the progress of construction community changing awareness, needs and perspectives, advanced technology in construction and new level of knowledge. Unproven practices and the technology of building code development and implementation in case of insufficient and outdated codes, the use of unproven advanced codes of other countries, or the infringement of the existing codes, in most cases, could lead to a large number of shortcomings of minimum requirements of public health, safety and general welfare, and poor quality of buildings. Every aspect of a building code development and implementation practice could be influenced by insufficiencies and infringements in building codes/regulations that could cause buildings failures. Generally, the success of a building code development and implementation practice is directly connected with the involved insufficiencies and infringements in the framework of building code (legal, Administrative, technical, & social), i.e. faults of building code development and implementation should be successfully resolved in order to come to an end of a building project assuring code's objectives (public health, safety and general welfare). One of the early research problems of building code development and implementation practice was conducted by Productivity Commission (2004) where the research organized and categorized the causes of shortcomings of BC according to four main functions of building code, including legal, administrative, technical, and social functions. Productivity Commission Research had been the starting point of research problems of building codes in Kuwait. For the past 20 years, many researchers have high numbers of categories, components and rankings to explain different types of insufficiencies and infringements in building codes/regulations. However, these categories and rankings produce inconsistent and overlapping cause and impact factors. In addition, researchers and practitioners at this point tend to focus on the technical and administrative sides related to the issues of building codes development and implementation, and neglecting the importance of legal and social sides. Legal issues like finding a law to prepare and enforce building codes, cover of insurance companies, building materials testing system, weak regulations related issues, building specifications, and clarity of regulation texts; as well as social issues like community awareness, issuing and enforcing legal court rules, deterrent punishments for violators, violations or cheatings in related issues, all of these were deemed not that critical by most reviewers. The research is specifically concerned with the insufficiencies and infringements in building codes/regulations which cause shortcomings of minimum requirements of public health, safety and general welfare, and how related cause and impact factors are selected and organized. Existing research highlights the need for further researches of how to relate between research and building regulations that are at present. There is evidence that construction industries around the world have little experience in this area (CIB TG37, 2001). The proposal within this research is to address this aspect of the debate by seeking to clarify the role of the four functions of building code; legal, administrative, technical, and social function as a frame of reference that stakeholder parties (building officials, design and construction professionals) might agree with and which should act as the basis for the selection and formation of occurrences of cause factors, and their iv impact on public health, safety and general welfare. The focus on the four functions of building code as a fault (cause) frame of reference potentially leads to a common, practical view of the (multi) dimensionality setting of fault (cause) within which cause factors may be identified and which, we believe, could be grounded across a wide range of practices specifically in this research of building code development and implementation. The research surveyed and examined the opinions of building officials, design and construction professionals. We assess which fault (cause) factors are most likely to occur in building and construction projects; evaluate fault (cause) impact by assessing which fault (cause) factors that building officials, design and construction professionals specifically think are likely to arise in the possibility of shortcomings of minimum requirements of public health, safety and general welfare. The data obtained were processed, analyzed and ranked. By using the EXCEL and SPSS for factor analysis, all the fault (cause) factors were reduced and groups into clusters and components for further correlation analysis. The analysis was able to prove an opinion on fault (cause) likelihood, the impact of the fault (cause) on the objectives of building code. The analysis indicates that it is possible to identify grouping of insufficiencies and infringements in building codes/regulations that is correspondent to the different parts of the framework of building code (legal, Administrative, technical, & social) these suggest three identified groups when viewing cause from the likelihood occurrence and four identified groups and their impact for each building code objective. The evidence related to the impact of building code objectives, view of cause, and provides a stronger view of which components of cause were important compared with cause likelihood. The research accounts for the difference by suggesting that a more selection and formation of cause and impact, offered by viewing cause within the context of a framework of building code, and viewing impact within the context of building code objectives (public health, safety and general welfare) allows those involved in building code development and implementation to have an understandable view of the relationships within cause factors, and between cause and impact factors. It also allows the various cause components and the associated emergent clusters to be more readily identified. The contribution of the research relates to the assessment of cause within a construction that is defined in the context of a fairly broad accepted view of the framework of building code (legal, Administrative, technical, & social). The fault (cause) likelihood construction is based on the building code framework proposed in this research and could facilitates a focus on roles and responsibilities, and allows the coordination and integration of activities for regular development and implementation with the building code goals. This contribution would better enable building officials and code writers to identify and manage faults (causes) as they emerge with BC aspects/parts and more closely reflect building and construction activities and processes and facilitate the fault (cause) administration exercise.
29
Abdallah, Saeed. "Widely linear minimum variance channel estimation with application to multicarrier CDMA systems." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=112550.
Анотація:
Conventional Minimum-Variance (MV) channel estimation is affected by two sources of error, namely the finite number of samples used to estimate the covariance matrix and the asymptotic bias due to interference and additive noise. On the other hand, widely linear (WL) filtering has been shown to improve the estimation of improper complex signals. Researchers have recently demonstrated that the application of WL processing principles can significantly improve the performance of subspace-based channel estimation algorithms. However, in contrast to MV estimation algorithms, subspace-based algorithms assume knowledge of the total number of users in the system, and must be coupled with sophisticated user enumeration algorithm at the expense of increased complexity. In this work, in an effort to combine the practical advantages of MV channel estimation algorithms with the performance of WL filters we propose a widely linear version of the MV channel estimator in the context of multicarrier(MC) CDMA systems employing real modulation. We use numerical simulations to demonstrate that the widely linear minimum-variance algorithm yields more accurate channel estimates compared to the conventional MV algorithm. By considering two simplified transmission/reception models, we also show analytically that the widely linear estimator on average reduces both types of error.
30
Zeh, Alexander. "Algebraic Soft- and Hard-Decision Decoding of Generalized Reed--Solomon and Cyclic Codes." Phd thesis, Ecole Polytechnique X, 2013. http://pastel.archives-ouvertes.fr/pastel-00866134.
Анотація:
Deux défis de la théorie du codage algébrique sont traités dans cette thèse. Le premier est le décodage efficace (dur et souple) de codes de Reed--Solomon généralisés sur les corps finis en métrique de Hamming. La motivation pour résoudre ce problème vieux de plus de 50 ans a été renouvelée par la découverte par Guruswami et Sudan à la fin du 20ème siècle d'un algorithme polynomial de décodage jusqu'au rayon Johnson basé sur l'interpolation. Les premières méthodes de décodage algébrique des codes de Reed--Solomon généralisés faisaient appel à une équation clé, c'est à dire, une description polynomiale du problème de décodage. La reformulation de l'approche à base d'interpolation en termes d'équations clés est un thème central de cette thèse. Cette contribution couvre plusieurs aspects des équations clés pour le décodage dur ainsi que pour la variante décodage souple de l'algorithme de Guruswami--Sudan pour les codes de Reed--Solomon généralisés. Pour toutes ces variantes un algorithme de décodage efficace est proposé. Le deuxième sujet de cette thèse est la formulation et le décodage jusqu'à certaines bornes inférieures sur leur distance minimale de codes en blocs linéaires cycliques. La caractéristique principale est l'intégration d'un code cyclique donné dans un code cyclique produit (généralisé). Nous donnons donc une description détaillée du code produit cyclique et des codes cycliques produits généralisés. Nous prouvons plusieurs bornes inférieures sur la distance minimale de codes cycliques linéaires qui permettent d'améliorer ou de généraliser des bornes connues. De plus, nous donnons des algorithmes de décodage d'erreurs/d'effacements [jusqu'à ces bornes] en temps quadratique.
31
Dang, Xiaoyu. "An Optimum Detector for Space-Time Trellis Coded Differential MSK." International Foundation for Telemetering, 2007. http://hdl.handle.net/10150/604515.
Анотація:
ITC/USA 2007 Conference Proceedings / The Forty-Third Annual International Telemetering Conference and Technical Exhibition / October 22-25, 2007 / Riviera Hotel & Convention Center, Las Vegas, NevadaThe accuracy of channel estimation plays a crucial role in the demodulation of data symbols sent across an unknown wireless medium. In this work a new analytical expression for the channel estimation error of a multiple input multiple output (MIMO) system is obtained when the wireless medium is continuously changing in the temporal domain. Numerical examples are provided to illustrate our findings. Space-time (ST) coding using Continuous Phase Modulation (CPM) has spectral advantages relative to linear modulations. In spite of the spectral benefits, Space-Time Trellis Codes (STTC) using the CPM implementation of Minimum Shift Keying (MSK) scheme has inherent inphase and quadrature interference, when the received complex baseband signal is the input into the matchfilter to remove the shaped sinusoid pulses. In this paper a novel optimum transmitting and detecting structure for STTC-MSK is proposed. Treating the Alamouti scheme as an outer code, each STTC MSK waveform frame is immediately followed by the orthogonal conjugate waveform frame at the transmit side. At the receiver first orthogonal wave forming is applied, then a new time-variant yet simple trellis structure of the STTC-MSK signals is developed. This STTC-MSK detector is absolutely guaranteed to be I/Q interference-free and still keeps a smaller computation load compared with STTC-QPSK. Simulations are made over quasi-static AWGN fading channel. It is shown that our detector for ST-MSK has solved the I/Q interference problem and has around 2.8 dB gain compared with the Alamouti Scheme and 3.8 dB gain for bit error rate at 5 X 10^(-3) in a 2 by 1 Multiple Input Single Output system.
32
Triantafillou, Thanasis C. (Thanasis Christos). "Failure mode maps and minimum weight design for structural sandwich beams with rigid foam cores." Thesis, Massachusetts Institute of Technology, 1987. http://hdl.handle.net/1721.1/14944.
Анотація:
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Civil Engineering, 1987.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.
Bibliography: leaves 69-71.
by Thanasis C. Triantafillou.
M.S.
33
Merlino, Enzo Maria. "Fractional Perimeter and Nonlocal Minimal Surfaces." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021.
Анотація:
This work aims to present a study of the principal results about the fractional perimeter and the regularity theory of nonlocal minimal surfaces. The fractional perimeter is a variation of the classical notion of Caccioppoli perimeter, recently introduced by L. Caffarelli, J.-M. Roquejoffre and O. Savin, that takes into account also long-range point-wise interactions between sets, modulated by a kernel with polynomial decay. That type of nonlocal minimal surfaces arises naturally, for instance, in the study of fractals and phase transitions models. First of all, we de�fine the fractional perimeter, and applying classical direct methods of Calculus of Variations we prove existence and compactness results for the corresponding minimizers. Then we deal with the regularity properties of such objects. Finally, we study a calibration result concerning nonlocal perimeters within Carnot groups.
34
Garcia, Vitor Araujo. "Idempotentes centrais primitivos em algumas álgebras de grupos." Universidade de São Paulo, 2015. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-05102015-225032/.
Анотація:
O objetivo do trabalho é apresentar alguns resultados acerca de anéis de grupos e aplicações, segundo o que foi estudado em livros e artigos sobre o assunto. Inicialmente, apresentaremos alguns fatos básicos sobre anéis de grupos, que podem ser encontrados em [5], e em seguida, apresentaremos os resultados principais, mais recentes, que foram estudados em dois artigos diferentes. No primeiro artigo [4], apresentou-se uma forma de calcular o número de componentes simples de certas álgebras de grupos abelianos finitos, bem como também foi apresentada uma forma de calcular geradores idempotentes de códigos abelianos minimais, suas dimensões e seus pesos. No segundo artigo [2], encontra-se uma descrição feita dos idempotentes centrais primitivos da álgebra de grupo racional de grupos nilpotentes finitos.Our goal in this project is to present some results about group rings and its applications, as presented in books and articles about this subject. First of all we are going to establish some basic fact about group rings, which can be found mainly in [5], and then we will present the main results, which are more recent, and have been studied in two different articles. In [4], the authors presented a way of evaluating the number of simple components of some finite group algebras, as well presented a way of evaluating idempotent generators of some minimal abelian codes, their dimension and their weights. In [2] there is a complete description of all the primitive central idempotents of the rational group algebra of finite nilpotent groups.
35
Su, Yong. "Mathematical modeling with applications in high-performance coding." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1127139848.
Анотація:
Thesis (Ph. D.)--Ohio State University, 2005.Title from first page of PDF file. Document formatted into pages; contains xiv, 130 p.; also includes graphics (some col.). Includes bibliographical references (p. 125-130). Available online via OhioLINK's ETD Center
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Garcia-Alis, Daniel. "On adaptive MMSE receiver strategies for TD-CDMA." Thesis, University of Strathclyde, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.366896.
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Sepúlveda, Castellanos Alonso. "Sobre codigos hermitianos generalizados." [s.n.], 2008. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307073.
Анотація:
Orientador: Fernando Eduardo Torres OrihuelaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
Made available in DSpace on 2018-08-10T07:01:07Z (GMT). No. of bitstreams: 1 SepulvedaCastellanos_Alonso_D.pdf: 783003 bytes, checksum: 2af4bba938cd5b7d31fcd02a5c79ac85 (MD5) Previous issue date: 2008
Resumo: Estudamos os códigos de Goppa (códigos GH) sobre certos corpos de funções algébricas com muitos lugares racionais. Estes códigos generalizam os bem conhecidos códigos Hermitianos; portanto podemos esperar que estes códigos tenham bons parâmetros. Bulygin (IEEE Trans. Inform. Theory 52 (10), 4664¿4669 (2006)) inicia o estudo dos códigos GH; enquanto Bulygin considerou somente característica par, nosso trabalho 'e feito em qualquer característica. Em qualquer caso, nosso trabalho é fortemente influenciado pelo de Bulygin. A seguir, listamos alguns dos nossos resultados com respeito aos códigos GH. ¿ Calculamos ¿distâncias mínimas exatas¿, em particular, melhoramos os resultados de Bulygin; ¿ Encontramos cotas para os pesos generalizados de Hamming, al'em disso, mostramos um algoritmo para aplicar estes cálculos na criptografia; ¿ Calculamos um subgrupo de Automorfismos; ¿ Consideramos códigos em determinados subcorpos dos corpos usados para construir os códigos GH
Abstract: We study Goppa codes (GH codes) based on certain algebraic function fields whose number of rational places is large. These codes generalize the well-known Hermitian codes; thus we might expect that they have good parameters. Bulygin (IEEE Trans. Inform. Theory 52 (10), 4664¿4669 (2006)) initiate the study of GH-codes; while he considered only the even characteristic, our work is done regardless the characteristic. In any case our work was strongly influenced by Bulygin¿s. Next we list some of the results of our work with respect to GH-codes. ¿ We calculate ¿true minimum distances¿, in particular, we improve Bulygin¿s results; ¿ We find bounds on the generalized Hamming weights, moreover, we show an algorithm to apply these computations to the cryptography; ¿ We calculate an Automorphism subgroup; ¿ We consider codes on certain subfields of the fields used for to construct GH-codes
Doutorado
Algebra (Geometria Algebrica)
Doutor em Matemática
38
Karaer, Arzu. "Optimum bit-by-bit power allocation for minimum distortion transmission." Texas A&M University, 2005. http://hdl.handle.net/1969.1/4760.
Анотація:
In this thesis, bit-by-bit power allocation in order to minimize mean-squared error (MSE) distortion of a basic communication system is studied. This communication system consists of a quantizer. There may or may not be a channel encoder and a Binary Phase Shift Keying (BPSK) modulator. In the quantizer, natural binary mapping is made. First, the case where there is no channel coding is considered. In the uncoded case, hard decision decoding is done at the receiver. It is seen that errors that occur in the more significant information bits contribute more to the distortion than less significant bits. For the uncoded case, the optimum power profile for each bit is determined analytically and through computer-based optimization methods like differential evolution. For low signal-to-noise ratio (SNR), the less significant bits are allocated negligible power compared to the more significant bits. For high SNRs, it is seen that the optimum bit-by-bit power allocation gives constant MSE gain in dB over the uniform power allocation. Second, the coded case is considered. Linear block codes like (3,2), (4,3) and (5,4) single parity check codes and (7,4) Hamming codes are used and soft-decision decoding is done at the receiver. Approximate expressions for the MSE are considered in order to find a near-optimum power profile for the coded case. The optimization is done through a computer-based optimization method (differential evolution). For a simple code like (7,4) Hamming code simulations show
that up to 3 dB MSE gain can be obtained by changing the power allocation on the
information and parity bits. A systematic method to find the power profile for linear block codes is also introduced given the knowledge of input-output weight enumerating function of the code. The information bits have the same power, and parity bits
have the same power, and the two power levels can be different.
39
Moro, Eliton Mendonça [UNESP]. "Códigos de bloco espaço-temporais via corpos quadráticos." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/148757.
Анотація:
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Os sistemas de comunicação com Múltiplas Entradas e Múltiplas Saídas (MIMO), são sistemas constituídos por estruturas que utilizam várias antenas, tanto no transmissor como no receptor. Por serem transmitidos via antenas, naturalmente surgem problemas de ruídos e de multipercursos, que impõe um desafio para o desenvolvimento dos sistemas de comunicação MIMO. Por esses motivos, muitos estudos focam em certas propriedades dos sinais enviados a fim de minimizar os efeitos sofridos na informação durante a transmissão. Existem muitos tipos diferentes de Códigos de Bloco Espaço-Temporais (STBC) disponíveis para duas antenas transmissoras, dentre eles, o código de bloco espaço-temporal ciclotômico, Código de Ouro e Código de Prata. Neste trabalho apresentamos uma construção de STBC cujos os sinais utilizados na transmissão são identificados por elementos de anéis de inteiros de corpos de números totalmente imaginários, Q(√d), com d<0, e apresentamos os melhores STBC em termos do critério que denominamos como critério produto, considerando extensões de Q(√d) com d=-1,-2,-3,-7, -11.
The communication systems of Multiple Input and Multiple Output (MIMO), are systems consisting of structures that use multiple antennas, both on the transmitter and the receiver. For being transmitted via antennas, noise and path problems naturally arise, which poses a challenge for the development and optimization of MIMO systems. For these reasons, many studies focus on certain properties of the signals sent in order to minimize the effects suffered on the information during transmission. There are many different types of Space-Time Block Codes (STBC) available for two transmitting antennas, such as the cyclotomic space-time block code, Golden code, and Silver code. In this work, we present a STBC construct via totally imaginary quadratic fields, Q(√d) with d <0 and present the best STBC in terms of the criterion that we call product criteria, considering extensions of Q(√d) with d = -1, - 2, - 3, - 7, -11.
40
Ghayour, Mehdi. "Enhancements to the sample-matrix-inversion based minimum- variance-distortionless-response detectors in code-division- multiple-access systems." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=18464.
Анотація:
Alternative methods to minimum-variance distortionless-response (MVDR) detection under small data records in code-division multiple-access binary phase-shift keying systems are explored. A comprehensive review of the conventional and optimal detectors as well as the principal component, cross-spectral and auxiliary vector (AV) methods are presented. The concept of widely linear (WL) filtering is introduced. Two different versions of the WL MVDR filters are proved to be equivalent; implementing the WL MVDR detector using the AV structure is proposed and shown to provide significant performance gain. We also propose two novel methods to implement the WL and plain MVDR detectors. One, based on the idea of limiting the eigenvalues of the sample correlation matrix, is outperformed by the AV implementation. The other method approximates the inverse of sample correlation matrix by inverting its eigenvalues using a polynomial function; it outperforms the AV implementation in terms of complexity while providing similar performances.Cette thèse explore de nouvelles méthodes d'amélioration de la performance du détecteur MVDR dans des systèmes DS-CDMA BPSK lorsque le nombre de vecteurs reçus utilisés pour estimer la matrice de corrélation est peu élevé. Une analyse des détecteurs conventionnel et optimal ainsi que les méthodes principal component (PC), cross-spectral (CS) et auxiliary vector(AV) sont présentés. Le concept de filtrage widely linear (WL) est introduit. L'équivalence de deux versions différentes du filtre WL MVDR est démontrée. La réalisation du détecteur WL MVDR utilisant une structure AV est proposée et le gain de performance significatif accompli par ce détecteur est prouvé. Nous proposons aussi deux nouvelles méthodes de réalisation des filtres MVDR WL et régulier. La première méthode, basé sur l'idée de limiter les valeurs propres de la matrice de corrélation estimée, est moins performante que la méthode AV. L'autre méthode obtient une approximation de l'inverse de la matrice de corrélation estimée en inversant ses valeurs propres l'aide d'une fonction polynomiale. Cette méthode est meilleure que la méthode AV en terme de complexité tout en présentant des performances similaires.
41
SILVA, JORGE KENEDY ALMEIDA. "TECHNICAL REGULATION: PROPOSITION OF A MINIMUM CODE OF THE GOOD REGULATORY PRACTICES AND DIAGNOSIS OF THE BRAZILIAN SYSTEM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=9964@1.
Анотація:
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOObjetivo: Proposição de um código mínimo das boas práticas da regulamentação técnica com vistas a disciplinar o desenvolvimento e a aplicação de regulamentos e assegurar que estes somente sejam introduzidos quando justificados com base em objetivos legítimos e em benefício da eficiência de qualquer sistema regulatório, com o propósito de evitar barreiras desnecessárias ao comércio e sem prejuízo dos interesses públicos. Motivação: Contribuir para o avanço do conhecimento sobre regulamentação técnica e para o aprimoramento das práticas regulatórias do sistema brasileiro, assim facilitando a inserção comercial do País em âmbito internacional. Contextualização: O trabalho se desenvolveu no contexto de um movimento mundial de harmonização de nomenclaturas e procedimentos regulatórios ainda em uso nos países membros da Organização Mundial do Comércio, reconhecendo-se, entretanto, que aspectos puramente técnicos não são capazes de justificar um modelo unificado. Metodologia: A proposição das boas práticas da regulamentação baseou-se: (i) na análise das características mínimas dos sistemas regulatórios em relação às recomendações da Organização Mundial do Comércio, do Código de Alfândega e de acordos comerciais regionais e internacionais de conceituados organismos; (ii) no diagnóstico da regulamentação técnica vigente no País à luz da prática internacional e na identificação dos diferentes atores que integram o sistema regulatório brasileiro; e (iii) na identificação dos aspectos funcionais e na eficácia do sistema regulatório brasileiro, por meio de pesquisa de campo conduzida junto aos 29 organismos que integram o referido sistema. Resultados: À luz da prática internacional, o trabalho identifica, discute e fundamenta um conjunto de nove parâmetros considerados essenciais às boas práticas da regulamentação, a saber: (i) aderência aos preceitos básicos e nomenclatura internacional; (ii) coordenação integrada do sistema nacional de regulamentação; (iii) sistemática para avaliação de riscos pela introdução ou não de um determinado regulamento técnico; (iv) infra-estrutura de comitês técnicos; (v) sistema nacional de normalização; (vi) sistema nacional de metrologia; (vii) infra-estrutura básica para avaliação da conformidade; (viii) redes de segurança do sistema regulatório e (ix) acompanhamento de mercado. Conclusões: A introdução de um código de boas práticas da regulamentação constitui pré-condição ao adequado funcionamento de qualquer sistema regulatório. Nove atributos essenciais foram caracterizados à luz da prática internacional como elementos que devem integrar um código mínimo capaz de proporcionar a harmonização entre os órgãos regulamentadores do país, a interação dos órgãos regulamentadores com o Ponto Focal Brasileiro, a promoção da cidadania, o desenvolvimento econômico e a redução dos impactos sócio- econômico-ambientalcultural da regulamentação técnica.
Objectives: The aim of this study is to formalize a set of rules, principles and instruments to suit the purpose of a good technical regulatory practice that would discipline the development and application of technical regulations based on legitimate objectives oriented by public interests. Such framework is required for the benefit of an efficient regulatory system to avoid unnecessary barriers to trade and without loss of public interests. Motivation: To contribute to the advance of technical regulation and best regulatory practices in Brazil, as a strategy to promote the country internationally. Context: The study was developed in the context of a worldwide movement, coordinated by the WTO, to harmonize nomenclature and procedures and to develop good regulatory practices, recognizing that purely technical aspects are not suffice to justify an unified approach. Methodology: The good regulatory practice here proposed is based on: (i) a diagnosis of technical regulation in place (ii) a search of the minimum characteristics of the regulatory systems in the light of WTO recommendations and relevant commercial agreements and (iii) a review of the specialized literaure and an exploratory survey among the regulatory bodies to find out their functional and operational aspects. Results: In the light of international practices, this work identifies, discusses and establishes a set of guiding principles considered essential to good regulatory practice, namely: (i) adherence to basic precepts and international practices; (ii) risk assessment associated with the introduction or not of a specific regulation; (iii) integrated coordination of a national system of regulation; (iv) infra-structure of national committees; (v) a national system of standardization; (vi) a national system of metrology; (vii) basic infra-structure for conformity assessment; (viii) security networks for the regulatory system and (ix) market surveillance. Conclusions: The introduction of a code of regulatory practices constitutes a pre-condition to an adequate functioning of any regulatory system. In the light of the best international regulatory practices, nine essential attributes were identified to promote harmonization of the regulatory bodies and information exchange between them; citizenship; economic development and reduction of their cultural, environmental, economic and social impacts.
42
Bezerra, Kelton Silva. "Rigidity and unstability of hypersurfaces and an unicity theorem on semi-Rieamannian manifolds." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=16530.
Анотація:
CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel SuperiorOur aim in this work is threefold. First, we get an extension, to the spherical case, of a theorem due to J. Simons, which concerns unstability of minimal cones constructed over a certain class of minimal submanifolds of the Euclidean sphere. Second, we classify the quasi-Einstein structures of the Riemannian product Hn x R. Third, we get a rigidity theorem for complete hypersurfaces into the De Sitter space, under certain conditions on the mean and scalar curvatures.
Este trabalho aborda trÃs problemas em Geometria Diferencial. Primeiro, obtemos uma extensÃo, para o caso esfÃrico, de um teorema devido a J. Simons sobre instabilidade de cones mÃnimos construÃdos sobre uma certa classe de subvariedades mÃnimas da esfera Euclidiana. Depois, classificamos as estruturas quasi-Einstein existentes sobre o produto Riemanniano Hn X R. Por fim, obtemos um teorema de rigidez para hipersuperfÃcies tipo-espaÃo completas do espaÃo de De Sitter, sob certas condiÃÃes sobre as curvaturas mÃdia e escalar, alÃm de uma condiÃÃo de integrabilidade.
43
Beirami, Ahmad. "Characterizing the redundancy of universal source coding for finite-length sequences." Thesis, Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/45750.
Анотація:
In this thesis, we first study what is the average redundancy resulting from the universal compression of a single finite-length sequence from an unknown source. In the universal compression of a source with d unknown parameters, Rissanen demonstrated that the expected redundancy for regular codes is asymptotically d/2 log n + o(log n) for almost all sources, where n is the sequence length. Clarke and Barron also derived the asymptotic average minimax redundancy for memoryless sources. The average minimax redundancy is concerned with the redundancy of the worst parameter vector for the best code. Thus, it does not provide much information about the effect of the different source parameter values. Our treatment in this thesis is probabilistic. In particular, we derive a lower bound on the probability measure of the event that a sequence of length n from an FSMX source chosen using Jeffreys' prior is compressed with a redundancy larger than a certain fraction of d/2 log n. Further, our results show that the average minimax redundancy provides good estimate for the average redundancy of most sources for large enough n and d. On the other hand, when the source parameter d is small the average minimax redundancy overestimates the average redundancy for small to moderate length sequences. Additionally, we precisely characterize the average minimax redundancy of universal coding when the coding scheme is restricted to be from the family of two--stage codes, where we show that the two--stage assumption incurs a negligible redundancy for small and moderate length n unless the number of source parameters is small.
%We show that redundancy is significant in the compression of small sequences. Our results, collectively, help to characterize the non-negligible redundancy resulting from the compression of small and moderate length sequences. Next, we apply these results to the compression of a small to moderate length sequence provided that the context present in a sequence of length M from the same source is memorized. We quantify the achievable performance improvement in the universal compression of the small to moderate length sequence using context memorization.
44
Irmer, Ralf. "Multiuser Transmission in Code Division Multiple Access Mobile Communications Systems." Doctoral thesis, Aachen : Shaker, 2005. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=013194664&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.
45
Irmer, Ralf. "Multiuser Transmission in Code Division Multiple Access Mobile Communications Systems." Doctoral thesis, Technische Universität Dresden, 2004. https://tud.qucosa.de/id/qucosa%3A24546.
Анотація:
Code Division Multiple Access (CDMA) is the technology used in all third generation cellular communications networks, and it is a promising candidate for the definition of fourth generation standards. The wireless mobile channel is usually frequency-selective causing interference among the users in one CDMA cell. Multiuser Transmission (MUT) algorithms for the downlink can increase the number of supportable users per cell, or decrease the necessary transmit power to guarantee a certain quality-of-service. Transmitter-based algorithms exploiting the channel knowledge in the transmitter are also motivated by information theoretic results like the Writing-on-Dirty-Paper theorem. The signal-to-noise ratio (SNR) is a reasonable performance criterion for noise-dominated scenarios. Using linear filters in the transmitter and the receiver, the SNR can be maximized with the proposed Eigenprecoder. Using multiple transmit and receive antennas, the performance can be significantly improved. The Generalized Selection Combining (GSC) MIMO Eigenprecoder concept enables reduced complexity transceivers. Methods eliminating the interference completely or minimizing the mean squared error exist for both the transmitter and the receiver. The maximum likelihood sequence detector in the receiver minimizes the bit error rate (BER), but it has no direct transmitter counterpart. The proposed Minimum Bit Error Rate Multiuser Transmission (TxMinBer) minimizes the BER at the detectors by transmit signal processing. This nonlinear approach uses the knowledge of the transmit data symbols and the wireless channel to calculate a transmit signal optimizing the BER with a transmit power constraint by nonlinear optimization methods like sequential quadratic programming (SQP). The performance of linear and nonlinear MUT algorithms with linear receivers is compared at the example of the TD-SCDMA standard. The interference problem can be solved with all MUT algorithms, but the TxMinBer approach requires less transmit power to support a certain number of users. The high computational complexity of MUT algorithms is also an important issue for their practical real-time application. The exploitation of structural properties of the system matrix reduces the complexity of the linear MUT mthods significantly. Several efficient methods to invert the ystem matrix are shown and compared. Proposals to reduce the omplexity of the Minimum Bit Error Rate Multiuser Transmission mehod are made, including a method avoiding the constraint by pase-only optimization. The complexity of the nonlinear methods i still some magnitudes higher than that of the linear MUT lgorithms, but further research on this topic and the increasing processing power of integrated circuits will eventually allow to exploit their better performance.Der codegeteilte Mehrfachzugriff (CDMA) wird bei allen zellularen Mobilfunksystemen der dritten Generation verwendet und ist ein aussichtsreicher Kandidat für zukünftige Technologien. Die Netzkapazität, also die Anzahl der Nutzer je Funkzelle, ist durch auftretende Interferenzen zwischen den Nutzern begrenzt. Für die Aufwärtsstrecke von den mobilen Endgeräten zur Basisstation können die Interferenzen durch Verfahren der Mehrnutzerdetektion im Empfänger verringert werden. Für die Abwärtsstrecke, die höhere Datenraten bei Multimedia-Anwendungen transportiert, kann das Sendesignal im Sender so vorverzerrt werden, dass der Einfluß der Interferenzen minimiert wird. Die informationstheoretische Motivation liefert dazu das Writing-on-Dirty-Paper Theorem. Das Signal-zu-Rausch-Verhältnis ist ein geeignetes Kriterium für die Performanz in rauschdominierten Szenarien. Mit Sende- und Empfangsfiltern kann das SNR durch den vorgeschlagenen Eigenprecoder maximiert werden. Durch den Einsatz von Mehrfachantennen im Sender und Empfänger kann die Performanz signifikant erhöht werden. Mit dem Generalized Selection MIMO Eigenprecoder können Transceiver mit reduzierter Komplexität ermöglicht werden. Sowohl für den Empfänger als auch für den Sender existieren Methoden, die Interferenzen vollständig zu eliminieren, oder den mittleren quadratischen Fehler zu minimieren. Der Maximum-Likelihood-Empfänger minimiert die Bitfehlerwahrscheinlichkeit (BER), hat jedoch kein entsprechendes Gegenstück im Sender. Die in dieser Arbeit vorgeschlagene Minimum Bit Error Rate Multiuser Transmission (TxMinBer) minimiert die BER am Detektor durch Sendesignalverarbeitung. Dieses nichtlineare Verfahren nutzt die Kenntnis der Datensymbole und des Mobilfunkkanals, um ein Sendesignal zu generieren, dass die BER unter Berücksichtigung einer Sendeleistungsnebenbedingung minimiert. Dabei werden nichtlineare Optimierungsverfahren wie Sequentielle Quadratische Programmierung (SQP) verwendet. Die Performanz linearer und nichtlinearer MUT-Verfahren MUT-Algorithmen mit linearen Empfängern wird am Beispiel des TD-SCDMA-Standards verglichen. Das Problem der Interferenzen kann mit allen untersuchten Verfahren gelöst werden, die TxMinBer-Methode benötigt jedoch die geringste Sendeleistung, um eine bestimmt Anzahl von Nutzern zu unterstützen. Die hohe Rechenkomplexität der MUT-Algorithmen ist ein wichtiges Problem bei der Implementierung in Real-Zeit-Systemen. Durch die Ausnutzung von Struktureigenschaften der Systemmatrizen kann die Komplexität der linearen MUT-Verfahren signifikant reduziert werden. Verschiedene Verfahren zur Invertierung der Systemmatrizen werden aufgezeigt und verglichen. Es werden Vorschläge gemacht, die Komplexität der Minimum Bit Error Rate Multiuser Transmission zu reduzieren, u.a. durch Vermeidung der Sendeleistungsnebenbedingung durch eine Beschränkung der Optimierung auf die Phasen des Sendesignalvektors. Die Komplexität der nichtlinearen Methoden ist um einige Größenordungen höher als die der linearen Verfahren. Weitere Forschungsanstrengungen an diesem Thema sowie die wachsende Rechenleistung von integrierten Halbleitern werden künftig die Ausnutzung der besseren Leistungsfähigkeit der nichtlinearen MUT-Verfahren erlauben.
46
David, Vincent. "Algorithmique parallèle sur les arbres de décision et raisonnement en temps contraint : étude et application au minimax." Toulouse, ENSAE, 1993. http://www.theses.fr/1993ESAE0008.
Анотація:
Cette thèse présente un modèle de traitement parallèle pour la mise en œuvre d'algorithmes de raisonnement dans le cadre d'un système temps-réel intelligent, et s'inscrit dans l'étude SATURNE menée au CERT-ONERA. Ce projet se fonde sur l'hypothèse que les tâches de traitement ont la capacité de s'adapter aux échéances temporelles. Pour satisfaire ce modèle, les solutions proposées sont la réduction de l'espace de recherche et l'accélération des traitements grâce au parallélisme. Ces changements devant intervenir durant l'exécution du processus, la gestion du parallélisme devient alors dynamique. Par ailleurs, les arbres de décision représentent une méthode fondamentale pour résoudre de nombreux problèmes d'intelligence artificielle, tels que la théorie des jeux à un joueur, les problèmes d'optimisation, la théorie des jeux à deux joueurs, les graphes Et/Ou et beaucoup d'autres problèmes NP-complets. Aussi, à partir de l'exemple de l'algorithme du minimax sur des arbres de jeux réels, une implémentation est réalisée sur Modulor, une machine à architecture distribuée à base de transputers développée au CERT-ONERA. La méthode de parallélisation se fonde sur une suppression du contrôle entre les processus de recherche, au profit d'un parallélisme spéculatif et du partage complet de l'information réalisé grâce à une mémoire physiquement distribuée mais virtuellement partagée. L’apport de notre approche pour les systèmes temps-réel distribués et tolérants aux fautes est évalué grâce aux résultats expérimentaux obtenus.
47
Ávila, Dane Marques de. "O segundo peso de Hamming do código de Reed-Muller generalizado." Universidade Federal de Uberlândia, 2016. https://repositorio.ufu.br/handle/123456789/16822.
Анотація:
Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorIn this work we present the determination of the second Hamming weight of generalized Reed- Muller codes in most cases (see Teorema 4.6). Our main reference is [13], although we have also used results from [3] and [5]. In the first chapter we describe finite fields e we show how they can be constructed. In chapter 2 we present the basics of coding theory. We define what are error correcting codes, the Hamming metric, the parameters of a code, the equivalence of codes through the concept of isometry, and we briefly present generalized Reed-Muller codes and their parameters. In chapter 3 we present some results from Grobner bases theory and the definition of Affine Cartesian codes, which generalize the generalized Reed-Muller codes. we use tools from Grobner bases theory to determine the dimension and the minimum distance of Affine Cartesian codes. We finish our work in chapter 4, with the determination of the second Hamming weight for generalized Reed-Muller codes in most cases.
Nesse trabalho apresentamos o cálculo do segundo peso de Hamming de códigos de Reed-Muller generalizados na maioria dos casos (v. Teorema 4.6). Nossa referência principal sera [13], embora tenhamos utilizado também resultados de [3] e [5]. No primeiro capítulo descrevemos os corpos finitos e mostramos como podem ser construídos. No capítulo 2 apresentamos os conceitos básicos da teoria de códigos. Nele, definimos o que são os códigos corretores de erros, a métrica de Hamming, os parâmetros de um código, a equivalência de códigos através da noção de isometria, bem como uma breve apresentação dos códigos de Reed-Muller generalizados e seus parâmetros. No capítulo 3 sao apresentados alguns resultados da teoria de Bases de Grobner e a definição dos Códigos Cartesianos Afins, que são uma generalização dos códigos de Reed-Muller generalizados. Usamos ferramentas da teoria de bases de Grobner para determinar a dimensão e distância mínima de Códigos Cartesianos Afins. Para finalizar nosso trabalho, no capítulo 4 determinamos o segundo peso de Hamming do Código de Reed-Muller generalizado na maioria dos casos.
Mestre em Matemática
48
Bernon, Jérémy. "Caractérisation du secteur de Higgs et aspects du problème de la saveur." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAY020/document.
Анотація:
Le Modèle Standard (MS) de la physique des particules s’est imposé comme étant la description la plus précise des interactions fondamentales entre les particules élémentaires. La découverte d’un boson de Higgs, avec une masse de 125 GeV, en Juillet 2012 au Large Hadron Collider (LHC), en a marqué sa confirmation définitive. Cependant, de nombreux problèmes observationnels et théoriques sont au coeur du MS, la plupart liés au secteur de Higgs. Etant une particule scalaire, le boson de Higgs souffre de très grandes corrections radiatives, ce qui déstabilise l’échelle électro-faible et mène au problème de hiérarchie. L’un des buts principaux du LHC est d’explorer précisément le secteur de Higgs, afin de caractériser le mécanisme à l’origine de la brisure de la symétrie électro- faible et de tester de possibles solutions au problème de hiérarchie. Le secteur de Higgs est également responsable de la génération des masses des fermions dans le MS, par le biais des couplages de Yukawa. Ces couplages sont extrêmement non génériques et cela mène aux problèmes de la saveur au delà du MS.La première partie de cette thèse se concentre sur la caractérisation précise du secteur de Higgs. En particulier, le code public Lilith est présenté, il permet de dériver des contraintes sur des scénarios de nouvelle physique à l’aide des mesures des propriétés du boson de Higgs en collisionneurs. Une analyse des couplages du boson de Higgs dans le contexte de plusieurs scénarios est ensuite effectuée. Dans la seconde partie, la phénoménologie des modèles à deux doublets de Higgs est étudiée à la lumière des résultats de la première phase du LHC. La limite d’alignement, ainsi que la possible présence de bosons de Higgs légers, sont étudiées en détail. Finalement, dans la dernière partie de cette thèse, l’hypothèse de Violation Minimale de la Saveur est introduite comme une solution potentielle aux problèmes de la saveur au delà du MS. Appliquée au Modèle Standard Supersymétrique Minimal, l’évolution des couplages baryoniques violant la parité R sous le groupe de renormalisation est analysée en détailThe Standard Model (SM) of particle physics stands as the most successful description of the fundamental interactions between elementary particles. The discovery of a Higgs boson, at a mass of 125 GeV, in July 2012 at the Large Hadron Collider (LHC), marked its ultimate confirmation. However, various observational and theoretical problems lie in the heart of the SM, with the majority of them linked to the Higgs sector. Being a scalar, the Higgs boson is subject to very large radiative corrections and this ultimately leads to the electroweak hierarchy problem. One of the main goals of the LHC program is to precisely probe the Higgs sector, in order to characterize the mechanism at the origin of the breaking of the electroweak symmetry and test possible solutions to the hierarchy problem. The Higgs sector is also responsible for the generation of the fermion masses, as it induces the Yukawa couplings. The SM flavor sector is highly hierarchical and this leads to flavor puzzles in theories beyond the SM.The first part of this thesis is dedicated to the precise characterization of the Higgs sector. In particular, the public tool Lilith is presented, which allows to derive constraints on new physics models based on the Higgs measurements at colliders. It is then used to perform global fits of the Higgs couplings in the context of various scenarios. In the second part, the phenomenology of two-Higgs-doublet models is studied in the light of the results from the first run of the LHC. The so-called alignment limit is explored in detail, as well as the possible presence of light scalar states. Finally, in the last part of this thesis, the Minimal Flavor Violation hypothesis is introduced as a possible solution to the flavor puzzles beyond the SM. Enforcing it in the Minimal Supersymmetric Standard Model, the renormalisation group evolution of the baryonic R-parity violating couplings is then studied in detail
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Oliveira, Fabrício Alves. "Códigos parametrizados afins." Universidade Federal de Uberlândia, 2014. https://repositorio.ufu.br/handle/123456789/16809.
Анотація:
Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorIn this work, we present a special class of linear codes: parameterized affine codes. We show that these codes are easy to construct and that given a parameterized affine code one can easily obtain an equivalent projective parameterized code equivalent to it. We also studied some topics which served as the theoretical foundations for the work, such as the theory of Groebner Bases, the footprint of an ideal and some topics of algebraic geometry and commutative algebra. This work has as main goal to obtain the basic parameters (length, dimension and minimum distance) of parameterized codes related and also to relate them to the projective parameterized codes, as done in [7]. We finish by applying the theory of Groebner Bases to the footprint of a certain ideal in order to obtain the basic parameters of the parameterized code over an affine torus.
Neste trabalho apresentamos uma classe especial de códigos lineares: os códigos parametrizados afins. Mostramos que esses códigos são de fácil construção e que, dado um código parametrizado afim, pode-se facilmente obter um código parametrizado projetivo equivalente a ele. Também estudamos algumas teorias que nos serviram como base teórica tais como: a teoria de Bases de Groebner e a Pegada de um ideal e alguns tópicos de geometria algébrica e álgebra comutativa. Este trabalho tem por objetivo principal obter os parâmetros básicos (comprimento, dimensão e distância mínima) dos códigos parametrizados afins e relacioná-los com os códigos parametrizados projetivos, assim como na referência [7]. Encerramos aplicando a teoria de Bases de Groebner a Pegada de um ideal para obter os parâmetros básicos do código parametrizado no toro afim.
Mestre em Matemática
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Marachli, Alaa. "Sur la stabilité de certaines surfaces minimales sous le flot de courbure moyenne nulle dans l'espace de Minkowski." Thesis, Paris Est, 2019. http://www.theses.fr/2019PESC0034.
Анотація:
Cette thèse porte sur la question de stabilité de certaines surfaces minimales évoluant sous le flot de courbure moyenne nulle dans l'espace de Minkowski. Cette problématique conduit à l'étude d'un système d'équations qui s'avère d'être hyperbolique sous la condition que les surfaces en question restent de type temps.Le travail qu'on présente ici se compose de deux parties. La première partie est liée à la formation de singularités en temps fini pour des surfaces asymptotiques au cône de Simons à l'infini et la seconde partie est consacrée à la stabilité de l'hélicoïde.Dans la première partie de cette thèse, on montre en collaboration avec Hajer Bahouri et Galina Perelman par une approche constructive l'existence d'une famille de surfaces évoluant par le flot de courbure moyenne nulle dans l'espace de Minkowski qui explose lorsque t tend vers 0 vers une surface qui se comporte comme le cône de Simons à l'infini. Ce problème revient à étudier les phénomènes d'explosion pour une équation d'ondes quasi linéaire du second ordre.L'objectif de la seconde partie est d’étudier la stabilité de l'hélicoïde soumise à des perturbations radiales normales. En fait, l'hélicoïde est linéairement instable d'indice 1 et c'est pourquoi on ne peut s'attendre à un résultat de stabilité pour des perturbations arbitraires. Nous montrons dans cette partie que cette instabilité est la seule obstruction pour la stabilité non linéaire globale de l'hélicoïde. Plus précisément, en se plaçant dans le cadre des perturbations radiales normales, on a démontré l'existence d'une variété de codimension 1 constituée de données initiales générant des solutions globales convergeant vers l'hélicoïde à l'infiniThis thesis focuses on the stability of some minimal surfaces under the vanishing mean curvature flow in Minkowski space. This issue amounts to investigate a system which turns out to be hyperbolic as long as the involved surfaces are time-like surfaces.The work presented here includes two parts. The first part in joint work with Hajer Bahouri and Galina Perelman is dedicated to the issue of singularity formation in finite time for surfaces asymptotic to the Simons cone at infinity and the second part is devoted to the study of the stability of the helicoid.In the first part of this thesis, we prove by a constructive approach the existence of a family of surfaces which evolve by the vanishing mean curvature flow in Minkowski space and which as t tends to~0 blow up towards a surface which behaves like the Simons cone at infinity. This issue amounts to investigate the singularity formation for a second order quasilinear wave equation.The aim of the second part is to investigate the stability of the helicoid under normal radial perturbations. Actually, the helicoid is linearly unstable of index 1, and that is why we cannot expect to have stability for arbitrary perturbations. In this part, we establish that this instability is the only obstruction to the global nonlinear stability for the helicoid. More precisely, in the framework of normal radial perturbations, we prove the existence of a codimension one set of small initial data generating global solutions converging to the helicoid at infinity