Dissertations / Theses on the topic 'Théorie des corps fins'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Théorie des corps fins.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
Duret, Jean-Louis. "Contributions à la théorie des modèles des corps commutatifs." Paris 7, 1992. http://www.theses.fr/1992PA077241.
Full textAngles, Bruno. "Modules de Drinfeld sur les corps finis." Toulouse 3, 1994. http://www.theses.fr/1994TOU30238.
Full textAllombert, Bill. "Théorie de Galois effective pour les corps de nombres et les corps finis : Développement du système PARI." Bordeaux 1, 2001. http://www.theses.fr/2001BOR12450.
Full textEsterle, Alexandre. "Groupes d'Artin et algèbres de Hecke sur un corps fini." Thesis, Amiens, 2018. http://www.theses.fr/2018AMIE0061/document.
Full textIn this doctoral thesis, we will determine the image of Artin groups associated to all finite irreducible Coxeter groups inside their associated finite Iwahori-Hecke algebra. This was done in type A in articles by Brunat, Marin and Magaard. The Zariski closure of the image was determined in the generic case by Marin. It is suggested by strong approximation that the results should be similar in the finite case. However, the conditions required to use are much too strong and would only provide a portion of the results. We show in this thesis that they are but that new phenomena arise from the different field factorizations. The techniques used in the finite case are very different from the ones in the generic case. The main arguments come from finite group theory. In high dimension, we will use a theorem by Guralnick-Saxl which uses the classification of finite simple groups to give a condition for subgroups of linear groups to be classical groups in a natural representation. In low dimension, we will mainly use the classification of maximal subgroups of classical groups obtained by Bray, Holt and Roney-Dougal for the complicated cases
Wen, Erzhuang. "Contribution à l'étude des codes correcteurs et des corps finis." Toulouse 3, 1994. http://www.theses.fr/1994TOU30255.
Full textDeschamps, Bruno. "Aspects de la théorie inverse de Galois." Lille 1, 1997. http://www.theses.fr/1997LIL10208.
Full textDans la troisieme partie nous generalisons la construction du corps q t r des nombres algebriques totalement reels. Nous y introduisons la notion de cloture totalement reelle d'un corps ordonnable k (notee $$ t r). Nous prouvons que dans les cas suivants: a) k corps reel clos, b) k corps de nombres ordonnable, c) k = k((x)) avec k reel clos ; le groupe de galois absolu de $$k t r(1) est pro-libre. Ce resultat constitue un analogue de la conjecture de shafarevich pour les corps $$k t r. D. Haran et m. Jarden ont recemment donne un exemple ou ce groupe n'est pas pro-libre. Nous conjecturons maintenant que cette propriete est vraie si k est denombrable et hilbertien. Nous completons ce travail par une etude du groupe de brauer de $$k t r, notamment nous prouvons que br(q t r) lim n , n(z/2) n. Pour finir nous presentons deux petits appendices. Le premier regarde sous plusieurs angles l'idee de probleme inverse a la theorie de galois. Le deuxieme essaie de generaliser la notion de corps pythagoriciens dont nous parlons un peu dans la troisieme partie
Sadi, Bounab. "Descente effective du corps de définition des revêtements." Lille 1, 1999. https://pepite-depot.univ-lille.fr/LIBRE/Th_Num/1999/50376-1999-127.pdf.
Full textAubry, Yves. "Variétés algébriques et corps de fonctions sur un corps fini." Habilitation à diriger des recherches, Aix-Marseille Université, 2002. http://tel.archives-ouvertes.fr/tel-00977396.
Full textMohamed, Ahmed Mohamed Saadbouh. "Modules de Drinfeld de rang 2 sur un corps fini." Aix-Marseille 2, 2004. http://www.theses.fr/2004AIX22022.
Full textArnaud, Nicolas. "Evaluation dérivée, multiplication dans les corps finis et codes correcteurs." Aix-Marseille 2, 2006. http://theses.univ-amu.fr.lama.univ-amu.fr/2006AIX22020.pdf.
Full textWe present an algorithm of multiplication in finite fields, based on an idea of G. V. And D. V. Chudnovsky. Our improvement is based on the use of derivated evaluations of functions on degree 1 and 2 places. This algorithm allows us to improve known bounds for the bilinear complexity of multiplication in some finite fields. We also present new constructions of correcting codes for the m-metrics, based on the recent work of Xing, Niederreiter, Ozbudak and Elkies on geometric codes. We also adapt a list decoding algorithm following ideas of Sudan in the case of m-metrics
Mkaouar, Mohamed. "Sur le développement en fraction continue de certaines séries formelles algébriques." Lyon 1, 1993. http://www.theses.fr/1993LYO10066.
Full textSZOPOS, Marcela. "Sur quelques questions de géométrie différentielle liées à la théorie des corps et des fils élastiques." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2005. http://tel.archives-ouvertes.fr/tel-00009754.
Full textOrange, Sébastien. "Calcul de corps de décomposition : utilisations fines d' ensembles de permutations en théorie de Galois effective." Paris 6, 2006. http://www.theses.fr/2006PA066307.
Full textSzopos, Marcela Gabriela. "Sur quelques questions de géométrie différentielle liées à la théorie des corps et des fils élastiques." Paris 6, 2005. https://tel.archives-ouvertes.fr/tel-00009754.
Full textOuld, Douh Mohamed. "Corps de fonctions cyclotomiques." Caen, 2012. http://www.theses.fr/2012CAEN2055.
Full textThe subject of this thesis is at the interface of number theory and algebraic geometry. The research work done in this thesis is in the arithmetic of function fields. Let Fq be a finite field having q elements and let T be an indetrminate over Fq: Let C be the Carlitz module which is a morphism of Fq-algebras from Fq[T] into the Fq-endomorphisms of the additive group given by C(T) = TX + Xq. The arithmetic of the fields generated over Fq(T) by the torsion points of C is a central subject in the arithmetic of function Fields. Since the last ten years, the theory has grown rapidly due to the important works of G. Anderson, D. Goss, M. Pappanikolas, L. Taelman , D. Thakur. The objective of this thesis is the arthmetic study of the module of units of Anderson-Taelman for Fq[T]. Let P be a prime of Fq[T]. We show that there exists a link between the P-adic behaviour of the module of units and the divisibility by P of a special value of the zeta function of Carlitz-Goss. In this thesis we give an geometric interpretation of this latter congruence in terms of the arithmetic of the jacobian of the Pth cyclotomic function field
Maalouf, Farès. "Structures C-minimales géométriques et trichotomie de Zilber." Paris 7, 2008. http://www.theses.fr/2008PA077174.
Full textThe main object of this thesis is the study of certain aspects of geometric C-minimal structures, i. E. Structures generalizing ultrametric structures, in which algebraic closure defines a notion of dimension on definable sets, and in which, uniformly in parameters, every definable subset of 1-space has a « simple form ». The main idea behind chapters 1-3 of this thesis is trying to construct algebraic structures (such as infinite groups and fields) in such structures which verify moreover some model theoretic assumptions. This kind of problems has already been suggested by Zilber for strongly minimal structures, and many results of Zilber's trichotomy are proved notably for Zariski geometries and o-minimal structures. In the first chapter, we classify up to elementarly equivalence, ail C-minimal vector spaces, which are the typical examples of the so called C-minimal locally modular structures. In the second chapter, we show how to construct an infinite type-definable group in any geometric non trivial locally modular C-minimal structure which is S\aleph_1S-saturated. In the third chapter, we show that for any algebraically closed valued field (a typical example of a geometric C-minimal structure), we can define multiplication on an open set in any non modular algebraic expansion of the vector space structure. Chapter four studies imaginaries in C-minimal vector spaces. We show how to find codes for some definable functions, without succeeding in the reach the final objective, which is weak elimination of imaginaries to the sort of clusters
Le, Yaouanc Erwan. "Problèmes de type Kummer-Vandiver dans les corps de fonctions." Caen, 2006. http://www.theses.fr/2006CAEN2067.
Full textLet us fix a prime number p. The famous conjecture of Vandiver predicts the nullity of the p-Sylow of the class group of the maximum totally real subfield of the pth cyclotomic number field. We study here analogues of this conjecture within the framework of the function fields over a finite field, or in other words, in positive characteristic. We recall in a first part the construction of the zeta functions of the functions fields over a finite field, then the construction of cyclotomic function fields. In a second part, we develop arithmetic technics specific to function fields. In particular, the use of Bernoulli's numbers enables us to transform the conjectures of algebraic nature, i. E. Concerning the fields, to conjectures of arithmetic nature, i. E. Formulated in terms of polynomials and numbers. This enables us, by the case of the quadratic fields to show the disability of a strong version of the analogue of the conjecture of Vandiver. We then state the conjecture of Goss that is a shrewd analogue of the conjecture of Vandiver which deals with to the components isotypic of the group of class. In a last part, we show that this conjecture is expressed in a simple and natural way within the framework of the Iwasawa's theory
De, Feo Luca. "Algorithmes Rapides pour les Tours de Corps Finis et les Isogénies." Phd thesis, Ecole Polytechnique X, 2010. http://tel.archives-ouvertes.fr/tel-00547034.
Full textNardi, Jade. "Quelques retombées de la géométrie des surfaces toriques sur un corps fini sur l'arithmétique et la théorie de l'information." Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30051.
Full textA part of this thesis, at the interface between Computer Science and Mathematics, is dedicated to the study of the parameters ans properties of Goppa codes over Hirzebruch surfaces. From an arithmetical perspective, the question about number of rational points of a variety defined over a finite field, which seemed dealt with by Lefchetz formula, regained interest thanks to error correcting codes. The minimum distance of an algebraic-geometric codes provides an upper bound of the number of rational points of a hypersurface of a given variety and with a fixed Picard class. Since reducible curves are most likely to reach this bound, one can focus on irreducible curves to get sharper bounds. A global strategy to bound the number of points on a variety depending on its ambient space and some of its geometric invariants is exhibited here. Moreover we develop a method for curves on toric surfaces by adapting F.J. Voloch et K.O. Sthör's idea on toric varieties. Finally, we interest in Private Information Retrivial protocols, which aim to ensure that a user can access an entry of a database without revealing any information on it to the database owner. A PIR protocol based on codes over weighted projective planes is displayed here. It enhances other protocols by offering a resistance to servers collusions, at the expense of a loss of storage capacity. This issue is fixed by a lifting process, which leads to asymptotically good families of codes, with the same local properties
Hanusse, Nicolas. "Cartes, constellations et groupes : questions algorithmiques." Bordeaux 1, 1997. http://www.theses.fr/1997BOR10646.
Full textParraud, Patrice. "Contributions a l'étude des suites quaternaires." Toulon, 1999. http://www.theses.fr/1999TOUL0011.
Full textOne of the problematics for communications systems in multiple access is the detection an the synchronization of messages numerically transmited. The purpose is to use some families of sequences which take value in a finite alphabet and have simultaneous good autocorrelation and good crosscorrelation properties. The goal of this work is thus a contribution in the study of quaternary periodic sequences with particular correlation properties. The first part is dedicated to new design of quaternary sequences by a general construction using the Gray map and some binary sequences. The second part is devoted to the study of quaternary periodic sequences with perfect autocorrelation properties. We give some non-existence results and a method to contruct some of them. In the third part, we establish some non-exi,stence results and using the previous general construction of the first part, give constructions for quaternary periodic sequences with almost-perfect auto-correlation properties. In the last part of this work, we caracterize some quaternary periodic sequences over a Galois ring using the trace map over the ring of integer modulus 4
Roche, Olivier. "Fusion d'un corps algébriquement clos avec un sous-groupe non-algébrique d'une variété Abélienne : corps octarines." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1097/document.
Full textWe construct fields of finite Morley rank with a predicate O foran infinite non-algebraic subgroup of a given simple Abelian variety A. Thefields we construct are strongly minimal when dim(A)>1, and of Morleyrank 2 when dim(A) = 1
Duarte, Mikaël. "Des corps en enfer. Une histoire des corps dans la région stéphanoise de la fin du XVIIIe à 1949." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSES014/document.
Full textAt the end of the eighteenth century, the population of the Stephan region was characterized by its mastery of industrial processes, a specific culture of the body, influenced by carnival rituals, the Jansenist convulsion movement, and then animal magnetism. lndustry then depends on the bodies of the workers, the Sublimes. The criticisms of the elites in the face of an industrial system pass !rom speeches to a slow interference in the workers' flesh, which must be locked up, controlled and rationalized. The disqualification of the workers' bodies begins with an aesthetic downgrading, which leads to racialization, reinforced by theories of degeneration. Rationalization, hygienic morality and physical education are part of this takeover of the flesh. The many resistance of the workers to an alienating mechanized and rationalized industrialization are characterized by a tenacious working-class counter-culture, the maintenance of small industry which maintains areas of freedom and violence, which passes through anarchism violate the strike, Shattered by a state repression
Diab, Menouer. "Contribution à l'étude des architectures systoliques pour les codes correcteurs d'erreurs." Toulouse 3, 1992. http://www.theses.fr/1992TOU30147.
Full textZayed, Maher. "Applications des ultraproduits aux représentations d'algèbres de dimension finie." Montpellier 2, 1988. http://www.theses.fr/1988MON20020.
Full textDicuangco, Lilibeth. "On duadic codes and split group codes." Nice, 2006. http://www.theses.fr/2006NICE4098.
Full textElbée, Christian d'. "Expansions et néostabilité en théorie des modèles." Thesis, Lyon, 2019. http://www.theses.fr/2019LYSE1076/document.
Full textThis thesis is concerned with the expansions of some algebraic structures and their fit in Shelah’s classification landscape. The first part deals with the expansion of a theory by a random –or generic– predicate for a substructure model of a reduct of the theory. We describe a setup allowing such an expansion to exist, which is suitable for several algebraic structures. In particular, we obtain the existence of additive generic subgroups of some theories of fields and multiplicative generic subgroups of algebraically closed fields in all characteristic. We also study the preservation of certain neostability notions, for instance, the NSOP 1 property is preserved but the simplicity is not in general. Thus, this construction produces new examples of NSOP 1 not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. The second part studies expansions of the groups of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of distinct p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to "reconstruct" the valuation using only the group operation
Zitouni, Mohammed. "L’étude et l’implémentation des algorithmes de couplages sur des courbes hyperelliptiques sur des corps premiers." Electronic Thesis or Diss., Paris 8, 2021. http://www.theses.fr/2021PA080031.
Full textLooking for new groups other than multiplicative group to design more constructive protocols in cryptography became the challenge since 2000. Several groups have emerged such as the group of rational points of an elliptic curve and the Jacobian of a hyperelliptic curve. Furthermore, pairings became even more practical tool to design new protocols in cryptography such as identity-based encryption and short signature. This thesis studies the implementation of pairing algorithms on hyperelliptic curves over prime fields. On the one hand, we regard the choice of the hyperelliptic curves to be used and the construction of genus two hyperelliptic curve of the ordinary Jacobian over a large prime field. On the other hand, we improve the pairing computations on different hyperelliptic curves. Tate pairing are implemented on ordinary Jacobian curves over a large prime field for several security levels. The optimization of the non negligible amount of operations that must be optimised to make the cost of using pairings in cryptography more reasonable. Finally, we give a concrete identity-based encryption scheme using the Tate pairing over genus two hyperelliptic curve
Koshelev, Dmitrii. "Nouvelles applications des surfaces rationnelles et surfaces de Kummer généralisées sur des corps finis à la cryptographie à base de couplages et à la théorie des codes BCH." Thesis, université Paris-Saclay, 2021. http://www.theses.fr/2021UPASM001.
Full textThere is well developed theory of so-called toric codes, i.e., algebraic geometry codes on toric varieties over a finite field. Besides ordinary (i.e., split) tori and toric varieties there are non-split ones. Therefore the thesis is dedicated to the study of algebraic geometry codes on the latter
Mihoubi, Cherif. "Trinômes irréductibles sur F2 et codes cycliques ternaires de rendements 1/2." Electronic Thesis or Diss., Paris, ENST, 2012. http://www.theses.fr/2012ENST0084.
Full textConsidering polynomials over the Galois finite fields for two elements, our intention stand over the divisibility of the trinomials x^am+x^bs+1, for m>s ≥ 1, by an irreducible polynomial of degree r, for this, we contribute to the result :If there exist positive integers m, s such that the trinomial x^am+x^bs+1 is divisible by an irreducible polynomial of degree r over F2, then a and b are not divisible by (2^r- 1). For this type of trinomials we conjectured that the ratios πM(a,b)/ πM(1,1) tend to a finite limit (dependently of a and b) when M tend to infinity. Our research stand at sequel on the cyclic codes of rate 1/2 over the two finite fields F3 and F5 and we check our research over whose are isodual. The so-called fundamental problem in coding theory is finding the largest value of dq for which a code of parameters [n, q, d] over Fq exists. In this context we have successfully optimize this distance for the cyclic codes of rate 1/2 over F3 and F5 up to length 74 for the ternary cyclic codes and 42 for whose over F5. We have also successful to construct seven classes of isodual cyclic codes over the field of 3 elements and three classes over the field of 5 elements
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.
Full textAlgebraic 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
Griffon, Richard. "Analogues du théorème de Brauer-Siegel pour quelques familles de courbes elliptiques." Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC084.
Full textThis thesis is devoted to the study of the arithmetic of elliptic curves E over function fields K in characteristic p>0 More precisely, we study the asymptotic behavious of their Brauer-Siegel ratio, denoted by BS(E/K). This invariant compares the product of its Néron-Tate regulator by the order of its Tate-Shafarevich group (assumed to be finite), to the differential height of E/K. The ratio BS(E/K) is defined in analogy with the quantity appearing in the classical Brauer-Siegel theorem for number fields. We prove that BS(E/K) has limit 1 (unconditionally) when E/K runs through one of five explicit families of elliptic curves. In other terms, those families satisfy a complete analogue of the Brauer-Siegel theorem. To prove such an analogue, we start by expressing the L-function of the relevant elliptic curves in terms of character sums over finite fields. Then, via the Birch and Swinnerton-Dyer conjecture, we link BS(E/K) to the "special value" L*(E/K, 1) of the L-function at s=1 (for the five families we study, this conjecture has been proved by D. Ulmer, T. Shioda,. . . ). It then remains to bound the size of L*(E/K, 1) : a good upper bound is easily proved, but the lower bound we require is more subtle. We thus develop tools to prove it : we express the q-adic valuation of a product of algebraic numbers (associated to Jacobi sums) and we prove an average equidistribution result for subgroups of (Z/dZ)*. We also obtain several auxiliary results on the Mordell-Weil rank, the torsion and the Tamagawa number of the elliptic curves we consider
Thomé, Emmanuel. "Théorie algorithmique des nombres et applications à la cryptanalyse de primitives cryptographiques." Habilitation à diriger des recherches, Université de Lorraine, 2012. http://tel.archives-ouvertes.fr/tel-00765982.
Full textBujard, Cédric. "Sous-groupes finis des groupes de stabilisateur étendus de Morava." Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00699844.
Full textMeziane, Chabane. "Modélisation mathématique et simulation numérique du transport mucociliaire." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM042.
Full textThe transport of biological fluid by the movement of cilia is a natural phenomenon found in almost all living beings. The aim of this thesis is the modeling and numerical simulation of mucociliary clearance, involving the action of cilia on the viscous fluid (composed of mucus and PCL), modeled by Stokes equations. As well as the secretion of mucus by the submucosal glands and the goblet cells, present in the bronchial epithelium. The first chapter deals with the 3D modeling of the fluid flow under the action of the cilia, the contribution of which is modeled by a 1D curve representing the central line of the cilium. The resulting problem is a singular and non-local Stokes problem. In Chapter 2, we studied in a model of a symmetrical dyadic bronchial tree, the thickness of the mucus layer at equilibrium, resulting from the secretion of mucus by the epithelium on the one hand, and from the evacuation of mucus through the cilia on the other hand. Finally, in Chapter 3, we studied the influence of airflow through the bronchial lumen on the efficiency of mucociliary clearance, and this, by considering a normal, strong, and extreme breathing regime
Walbrou, Sonny. "Pour une histoire critique au prisme des rapports du corps à la machine, entre le cinéma, jeu vidéo et culture spectaculaire fin-de-siècle : continuité critique, innervation, attraction." Thesis, Lille, 2018. http://www.theses.fr/2018LIL3H037.
Full textBetween past and present, between the turn-of-the-century spectacular culture, cinema and video games, our thesis explores the critical aspects of body-machine relationships understandings regarding Walter Benjamin’s concept of innervation. From a historiographical concept formulated within this work, i. e. “critical continuity” which consists in crafting permanencies though history, our purpose is to delineate an operating critic of the new media. From the concepts of innervation and critical continuity, we explore two defining “state of body” to draw resonances between past and present. One takes place at the turn of the century while the other takes place during the 1980’s. The former concerns the becoming-attraction of the machines circa 1900. Extending Tom Gunning’s concept, we understand such an attraction as a corporeal relationship between the spectator’s body and the machine. Through 1900’s visual and spectacular culture, we examine a recurring topos: the immobile voyage. We find and explore the critical topicality of such a topos up to present day as something that has never changed despite technical innovations. The latter state explores the transformations regarding the body-screen relationships in video game practice. We study a collection of representations appearing between the early 1980’s up to the middle of the 1990’s featuring another recurring topos: the screen crossed whether by the game’s universe whether by the player. These two topoi help us to conceive a critic of the new media on the very basis of novelty
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.
Full textRiss, Mariane. "Relevés d'isotypies et descentes de Shintani : le groupe symplectique de dimension 4 sur Fq,q impair." Paris 7, 2001. http://www.theses.fr/2001PA077114.
Full textGrenet, Bruno. "Représentations des polynômes, algorithmes et bornes inférieures." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00770148.
Full textCouvreur, Alain. "Résidus de 2-formes différentielles sur les surfaces algébriques et applications aux codes correcteurs d'erreurs." Phd thesis, Université Paul Sabatier - Toulouse III, 2008. http://tel.archives-ouvertes.fr/tel-00376546.
Full textMihoubi, Cherif. "Trinômes irréductibles sur F2 et codes cycliques ternaires de rendements 1/2." Thesis, Paris, ENST, 2012. http://www.theses.fr/2012ENST0084/document.
Full textConsidering polynomials over the Galois finite fields for two elements, our intention stand over the divisibility of the trinomials x^am+x^bs+1, for m>s ≥ 1, by an irreducible polynomial of degree r, for this, we contribute to the result :If there exist positive integers m, s such that the trinomial x^am+x^bs+1 is divisible by an irreducible polynomial of degree r over F2, then a and b are not divisible by (2^r- 1). For this type of trinomials we conjectured that the ratios πM(a,b)/ πM(1,1) tend to a finite limit (dependently of a and b) when M tend to infinity. Our research stand at sequel on the cyclic codes of rate 1/2 over the two finite fields F3 and F5 and we check our research over whose are isodual. The so-called fundamental problem in coding theory is finding the largest value of dq for which a code of parameters [n, q, d] over Fq exists. In this context we have successfully optimize this distance for the cyclic codes of rate 1/2 over F3 and F5 up to length 74 for the ternary cyclic codes and 42 for whose over F5. We have also successful to construct seven classes of isodual cyclic codes over the field of 3 elements and three classes over the field of 5 elements
Pinto, Castaneda Luis. "Amalgames de corps valués." Sorbonne Paris Cité, 2015. http://www.theses.fr/2015USPCC238.
Full textIn this thesis, we use the Fraïssé-Hrushovski amalgamation method in order to fuse valued fields, thus obtaining a first example of use of that technique in an unstable NIP context. Recall that in the 80's Hrushovski introduced a variation of Fraïssé's original method, building a counterexample to the trichotomy conjecture. W( first consider the fusion of algebraically closed fields of characteristic zero. We define a notion of space: they consist in vector spaces yielding, in a relational fashion, two field structures. After proving an asymetric amalgamation lemma for the class of finitely generated fusions and constructing its limit, we study the corresponding theory and compute its Morley (and Lascar) rank. We then examine the valued context, to whicl we extend numerous previous results under a pure separation hypothesis and with the choice of a suitable predimension. We show that the class of fusions of finite linear dimension and whose constant field is at most countable has the amalgamation property, but we are not able to construct the limit because of cardinality reasons (under our hypotheses). However, choosing an appropriate subclass, we obtain a rich fusion whose residual structure is precisely our non-valued limit
Ros, Nicolas. "Corps des modules et corps de définition de revêtements algébriques." Toulouse 3, 2004. http://www.theses.fr/2004TOU30288.
Full textLet k be a perfect field and let c be an algebraic closure of k, separably closed. Let also bk be a k-curve. We note bc the c-curve obtained from bk by extension of scalars. We study the category rev of c-covers over bc that is to say finite and etale morphisms over bc. If f is an object of rev, a field of definition of f is a field a c-cover isomorphic to f can be defined over. Furthermore, the group gal(c/k) acts on rev functorially ; for all s in gal(c/k), the cover s. F is the pull-back of f along spec(s). If, for all s in gal(c/k), s. F is c-isomorphic to f, k is said to be the field of moduli of f. That is a well-known fact that the field of moduli is the intersection of the fields of definition. However, we don't know if a c-cover which is defined over all the the completions kv of k (v valuation of k) - and so with field of moduli k - is necessarily defined over k. First, we describe a cohomological criterion in order to express the fact that a certain type of covers of bc is defined over a given field. Then, using the kummer's theory, we explain a method to construct covers (defined over k) over the projective line whose group of automorphisms is a given gal(c/k)-module. By means of the class field theory and the special cases of grunwald-wang's theorem, we construct a cover between curves which is defined over all the completions of the rationals field without being defined over the rationals field. In conclusion, we exhibit a violation of the local-global principle for the category rev
Zrelli, Yasamine. "Identification aveugle de codes correcteurs d'erreurs basés sur des grands corps de Galois et recherche d'algorithmes de type décision souple pour les codes convolutifs." Thesis, Brest, 2013. http://www.theses.fr/2013BRES0097/document.
Full textIn the first part of this thesis, we have focused on the blind identification of non-binary error correcting codes over the Galois field GF(2m). A study of the properties of Galois fields and non-binarycodes has been presented so as to get the essential elements for a blind identification of non-binary codes parameters. From the knowledge of only the received symbols, methods have been developed to identify the code parameters in the case of a noiseless transmission. The relevance of this approach has been highlighted when the parameters of the used Galois field are known bythe receiver. A theoretical study of rank criterion behaviors has been also presented to justify its use by the most existing identification methods. Then, three blind identification methods of the codeword size for binary and non-binary linear codes have been developped in the framework of a noisy transmission. In order to identify a dual code basis, an existing method for binary codes based on the use of a hard decision demodulation has been generalized to non-binary codes. The detection performance of this technique has been improved when an iterative process based on the joint use of a soft-decision demodulator and a soft-decision iterative decoding is introduced. In the second part of this thesis manuscript, a mathematical formalism is proposed in order to investigate the impact of mapping-demapping functions on linear algebra computations and properties over Galois field in the case of non-binary error correcting codes. Finally, this formalism has been exploited to detect or/and correct some digital transmission problems such as a bad synchronization. Finally, we have studied the impact of some mapping-demapping functions on the blind identification ofnon-binary error correcting codes parameters
Roussine, Sophie. "Sur le lambda-invariant des corps de nombres." Caen, 2012. http://www.theses.fr/2012CAEN2054.
Full textThis PhD report deals with the study of the Iwasawa lambda invariant λp(K) when p is an odd prime and K is an abelian number field over Q. At first, only the case where K is an imaginary quadratic field is considered. Let's remind us K. Horie's result : for a fixed prime number p, there are infinitely many imagi-nary quadratic fields K such that λp(K) = 0 ; and R. Greenberg's conjecture : λp(K) is not bounded when K runs over the set of imaginary quadratic fields and p runs over the set of prime numbers. In this PhD report, a criterion is given to determine if λp(K) = 1 when p is a fixed odd prime and K is an imaginary quadratic field in which p splits. This result is obtained via a fine study of a theorem of R. Gold. Then, in an other chapter, by analogy with results in function fields, a conjecture is formulated on the existence of a constant C(p) depending on p such that for every abelian number field K we would have λp(K) ≤ C(p)dKlog(dK) where dK is the absolute discriminant of the field K. The optimality of such a bound is studied, as well as how it is related to other conjectures
Jaoui, Rémi. "Flots géodésiques et théorie des modèles des corps différentiels." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLS147/document.
Full textThis thesis is dedicated to studying the interactions between two different approaches regarding differential equations: the model-theory of differentially closed fields on the one side and the dynamical analysis of real differential equations, on the other side. In the first chapter, we present a formalism from differential algebra, in terms of D-varieties à la Buium over the field of real numbers (endowed with the trivial derivation), that allows one to realise both approaches at the same time. The main result is a criterion of orthogonality to the constants, based on the topological dynamic of its associated real analytic flow. The second chapter is dedicated to the algebraic differential equations describing the (unitary) geodesic flow of a real algebraic variety endowed with an algebraic, non-degenerated symmetric 2-form. Using the previous criterion, we prove a theorem of orthogonality to the constants "in negative curvature'', that relies on the results of Anosov and of his followers, regarding the topological dynamic - the weakly mixing topological property - for the geodesic flow of a compact Riemannian manifold with negative curvature. In dimension 2, we conjecture a more precise description - its generic type is minimal and has a trivial pregeometry- for the structure associated to the unitary geodesic equation. In the third chapter, we present some motivations and partial results on this conjecture
Benoist, Franck. "Théorie des modèles des corps munis d'une dérivation de Hasse." Phd thesis, Université Paris-Diderot - Paris VII, 2005. http://tel.archives-ouvertes.fr/tel-00134889.
Full textRioux, Romain. "Théorie des modèles d'expansions de corps valués : phénomènes de séparation." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1157/document.
Full textThis thesis is dedicated to the model theoretic study of algebraically closed valued fields equipped with a additional unary predicate for either a multiplicative subgroup or a subfield.We give a result of relative quantifier elimination for structures of the kind (M , G), where M is an algebraically closed valued field and G is a multiplicative subgroup on wich the valuation is injective
Bengoechea, Paloma. "Corps quadratiques et formes modulaires." Paris 6, 2013. http://www.theses.fr/2013PA066425.
Full textThis thesis is devoted to the study of interactions between quadratic fields and modular forms. The first part is about real quadratic fields. We study how the theory of periods relates continued fractions and modular forms. Using reduction theories for binary quadratic forms of positive discriminant and Diophantine approximation on the projective real line, we prove some conjectures of Zagier and other unexpected results about certain real functions giving the even parts of the period polynomials of the modular forms which are the Fourier coefficients of the kernel function for the Shimura-Shintani lifts. We also improve a classic theorem of Serret on continued fractions. The second part is about imaginary quadratic fields. Modular forms related to Shimura-Shintani lifts appearing in the first part of the thesis arise from integral quadratic polynomials with positive discriminant. In the second part, we study the meromorphic analogues, with negative discriminant. Finally, we compute the Galois action on the special values of theta functions normalised by the Dedekind eta function using Shimura reciprocity law. As a consequence, we prove some experimental results of Cohen and Zagier and we deduce some results on the non-vanishing of these special theta values
Leduc, Éric. "Vers une théorie matérialiste du perfectionnement du jugement : corps de philosophe et philosophie du corps chez Diderot." Thesis, Université d'Ottawa / University of Ottawa, 2014. http://hdl.handle.net/10393/31838.
Full text