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Relevant bibliographies by topics / Extremal self-dual codes

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Academic literature on the topic 'Extremal self-dual codes'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Extremal self-dual codes"

1

Dougherty, S. T., T. A. Gulliver, and M. Harada. "Extremal binary self-dual codes." IEEE Transactions on Information Theory 43, no. 6 (1997): 2036–47. http://dx.doi.org/10.1109/18.641574.

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Dontcheva, R., and M. Harada. "New extremal self-dual codes of length 62 and related extremal self-dual codes." IEEE Transactions on Information Theory 48, no. 7 (July 2002): 2060–64. http://dx.doi.org/10.1109/tit.2002.1013144.

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Bouyuklieva, Stefka, Anton Malevich, and Wolfgang Willems. "Automorphisms of Extremal Self-Dual Codes." IEEE Transactions on Information Theory 56, no. 5 (May 2010): 2091–96. http://dx.doi.org/10.1109/tit.2010.2043763.

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Han, Sun-Ghyu, and June-Bok Lee. "NONEXISTENCE OF SOME EXTREMAL SELF-DUAL CODES." Journal of the Korean Mathematical Society 43, no. 6 (November 1, 2006): 1357–69. http://dx.doi.org/10.4134/jkms.2006.43.6.1357.

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Tsai, H. P. "Existence of certain extremal self-dual codes." IEEE Transactions on Information Theory 38, no. 2 (March 1992): 501–4. http://dx.doi.org/10.1109/18.119711.

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Han-Ping Tsai. "Existence of some extremal self-dual codes." IEEE Transactions on Information Theory 38, no. 6 (1992): 1829–33. http://dx.doi.org/10.1109/18.165461.

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Han-Ping Tsai and Yih-Jaw Jiang. "Some new extremal self-dual [58,29,10] codes." IEEE Transactions on Information Theory 44, no. 2 (March 1998): 813–14. http://dx.doi.org/10.1109/18.661527.

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Gulliver, T. Aaron, Masaaki Harada, and Jon-Lark Kim. "Construction of new extremal self-dual codes." Discrete Mathematics 263, no. 1-3 (February 2003): 81–91. http://dx.doi.org/10.1016/s0012-365x(02)00570-8.

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Koch, Helmut. "On self-dual doubly-even extremal codes." Discrete Mathematics 83, no. 2-3 (August 1990): 291–300. http://dx.doi.org/10.1016/0012-365x(90)90013-8.

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Spence, Edward, and Vladimir D. Tonchev. "Extremal self-dual codes from symmetric designs." Discrete Mathematics 110, no. 1-3 (December 1992): 265–68. http://dx.doi.org/10.1016/0012-365x(92)90716-s.

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Dissertations / Theses on the topic "Extremal self-dual codes"

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Malevich, Anton [Verfasser], and Wolfgang [Akademischer Betreuer] Willems. "Extremal self-dual codes / Anton Malevich. Betreuer: Wolfgang Willems." Magdeburg : Universitätsbibliothek, 2012. http://d-nb.info/1053914296/34.

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BORELLO, MARTINO. "Automorphism groups of self-dual binary linear codes with a particular regard to the extremal case of length 72." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2014. http://hdl.handle.net/10281/49887.

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Let C be a binary linear code and suppose that its automorphism group contains a non trivial subgroup G. What can we say about C knowing G? In this thesis we collect some answers to this question. We focus on the cases G = C_p, G = C_2p and G = D_2p (p an odd prime), with a particular regard to the case in which C is self-dual. Furthermore we generalize some methods used in other papers on this subject. The third chapter is devoted to the investigation of the automorphism group of a putative self-dual [72; 36; 16] code, whose existence is a long-standing open problem. Last chapter is about semi self-dual codes and new upped bound on their dual distance.

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Su, Wen-Ku, and 蘇文谷. "CONSTRUCT EXTREMAL SELF-DUAL CODES FROM NON-EXTREMAL SELF-DUAL CODES." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/aujcym.

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碩士
東吳大學
數學系
93
1.We constructed 17 extremal self-dual [66,33,12] codes with weight enumerator W1(y) and 19 extremal self-dual [66,33,12] codes with weight enumerator W3(y). 2.We constructed 27 extremal self-dual [68,34,12] codes with weight enumerator W1(y) and 64 extremal self-dual [68,34,12] codes with weight enumerator W2(y).

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Shih, Ming-Chih, and 施明志. "INEQUIVALENT CODES OF EXTREMAL SELF-DUAL CODES." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/07398386185225200279.

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HSU, HAO-CHUNG, and 徐浩鐘. "EXTREMAL SELF-DUAL CODES OF LENGTH 68." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/99390085693207554696.

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Wu, Ren-Yih, and 吳仁義. "Extremal Self-Dual Codes of Length 66." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/56088992181448892067.

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碩士
東吳大學
數學系
91
In Dougherty, Gulliver, and Harada [2] there are three possibilities for the weight enumerators of extremal self-dual [66,33,12] codes. Where β is an undetermined parameter. The code D16 constructed in Conway and Sloane [1] with β=0 in w1 . Also β=0 and β=66 were constructed in [3]. Two extremal self-dual [66,33,12] codes with weight enumerator w2 were constructed in Tsai [5]. A general method of construction of self-dual codes from a known [N,K,D] self-dual code with K is even has constructed by Harada [5]. We extend this method on K is odd and apply in K is odd.Apply those properties to find the self-dual code of length 66, we got new extremal self-dual [66,33,12] code with β=32 for w1 and at least 50 inequivalent extremal self-dual [66,33,12] codes with .At length 50, we got 3 inequivalent extremal self-dual [50,25,10] codes.

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Jiang, Yih-Jaw, and 姜義照. "Extremal Self-Dual Codes of Length 58." Thesis, 1996. http://ndltd.ncl.edu.tw/handle/78252984777614434121.

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碩士
東吳大學
數學系
85
The main purpose of this thesis is to obtain the following extremal self-dual codes of length 58 with weight enumerator W=1+(319-24β-2γ)y^10+(3132+152β+2γ)y^12+(36540-680β+18γ) y^14 +(299541+1832β-18γ)y^16+... .where (β=0,γ=88),(β=0, γ=90),(β=0,γ=92),(β=0,γ=102),(β=0,γ=104),(β=0,γ=106),( β=0,γ=108),(β=0,γ=110),(β=0,γ=112),(β=0,γ=114),(β=0, γ=116),(β=0,γ=118),(β=0,γ=120),(β=0,γ=122),(β=0, γ=124),(β=2,γ=62),(β=2,γ=64),(β=2,γ=68),(β=2,γ=70),( β=2,γ=72),(β=2,γ=74),(β=2,γ=76),(β=2,γ=78),(β=2, γ=80),(β=2,γ=82),(β=2,γ=84),(β=2,γ=86),(β=2,γ=88).

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Shih, Pei-Yu, and 施沛渝. "Extremal self-dual codes of lengh 60." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/98450279682727582732.

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Ouyang, Jung-Yan, and 歐陽中彥. "On the Classification of Binary Extremal Self-dual Codes." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/26168086921462710845.

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碩士
國立成功大學
數學系應用數學碩博士班
92
The object of this study is mainly discuss the binary extremal self-dual codes. For Type I codes, we are going to investigate the weight enumerators and relative data from length 2 to length 100. For Type II codes, we investigate those from length 8 to length 96.

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Hsu, Mu-Hsin, and 許睦鑫. "Extremal Self-Dual Codes of Lengths 54, 64, 66 and 68." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/35552907472067873200.

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Book chapters on the topic "Extremal self-dual codes"

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Kim, Jon-Lark. "Computer Based Reconstruction of Binary Extremal Self-dual Codes of Length 32." In Mathematical Software – ICMS 2014, 115–18. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44199-2_20.

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Camion, P., B. Courteau, and A. Monpetit. "Coset Weight Enumerators of the Extremal Self-Dual Binary Codes of Length 32." In Eurocode ’92, 17–29. Vienna: Springer Vienna, 1993. http://dx.doi.org/10.1007/978-3-7091-2786-5_2.

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Tonchev, Vladimir D. "Symmetric Designs without Ovals and Extremal Self-Dual Codes." In Combinatorics ′86, Proceedings of the International Conference on Incidence Geometries and Com binatorial Structures, 451–57. Elsevier, 1988. http://dx.doi.org/10.1016/s0167-5060(08)70268-1.

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Banek, Tadeusz, and Edward Kozlowski. "Active Learning in Discrete-Time Stochastic Systems." In Knowledge-Based Intelligent System Advancements, 350–71. IGI Global, 2011. http://dx.doi.org/10.4018/978-1-61692-811-7.ch016.

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A general approach to self-learning based on the ideas of adaptive (dual) control is presented. This means that we consider the control problem for a stochastic system with uncertainty as a leading example. Some system’s parameters are unknown and modeled as random variables with known a’priori distribution function. To optimize an objective function, a controller has to learn the system’s parameter values. The main difficulty comes from the fact that he has to optimize the objective function parallely, i.e., at the same time. Moreover, these two goals considered separately not necessarily coincide and the main problem in the adaptive control is to find the trade-off between them. Looking from the self-learning perspective the two directions are visible. The first is to extract the learning procedure from an optimal adaptive control law and to formulate it as a Cybernetic Principle of self-learning. The second is to consider a control problem with the special objective function. This function has to measure our knowledge about unknown parameters. It can be the Fisher information (Banek & Kulikowski, 2003), the joint entropy (for example Saridis, 1988; Banek & Kozlowski, 2006), or something else. This objective function in the control problem will force a controller to steer a system along trajectories that are rich in information about unknown quantities. In this chapter the authors follow the both directions. First they obtain conditions of optimality for a general adaptive control problem and resulting algorithm for computing extremal controls. The results are then applied to the simple example of the Linear Quadratic Gaussian (LQG) problem. By using analytical results and numerical simulations the authors are able to show how control actions depend on the a’piori knowledge about a system. The first conclusion is that a natural, methodological candidate for the optimal self-learning strategy, the “certainty equivalence principle”, fails to satisfy optimality conditions. Optimal control obtained in the case of perfect system’s knowledge is not directly usable in the partial information case. The need of active learning is an essential factor. The differences between controls mentioned above are visible on a level of computations and should be interpreted on a higher level of cybernetic thinking in order to give a satisfactory explanation, perhaps in the form of another principle. Under absence of the perfect knowledge of parameters values, the control actions are restricted by some measurability requirement and the authors compute the Lagrange multiplier associated with this “information constraint”. The multiplier is called a “dual” or “shadow” price and in the literature of the subject is interpreted as an incremental value of information. The authors compute the Lagrange multiptier and analyze its evolution to see how its value changes as the time goes on. As a second sort of conclusion the authors get the self-learning characteristic coming from the information theory point of view. In the last section the authors follow the second direction. In order to estimate the speed of self-learning they choose as an objective function, the conditional entropy. They state the optimal control problem for minimizing the conditional entropy of the system under consideration. Using general results obtained at the beginning, they get the conditions of optimality and the resulting algorithm for computing the extremal controls. Optimal evolution of the conditional entropy tells much about intensivity of self-learning and its time distribution.

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Conference papers on the topic "Extremal self-dual codes"

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Yorgova, Radinka. "Binary self-dual extremal codes of length 92." In 2006 IEEE International Symposium on Information Theory. IEEE, 2006. http://dx.doi.org/10.1109/isit.2006.262034.

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Yorgova, Radinka, and Nuray At. "On extremal binary doubly-even self-dual codes of length 88." In 2008 International Symposium on Information Theory and Its Applications (ISITA). IEEE, 2008. http://dx.doi.org/10.1109/isita.2008.4895444.

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