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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: 31 July 2025

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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 (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 (2010): 2091–96. http://dx.doi.org/10.1109/tit.2010.2043763.

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Han, Sunghyu. "Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4)." Information 9, no. 7 (2018): 172. http://dx.doi.org/10.3390/info9070172.

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Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over GF(2) and GF(4) with minimal shadow. In particular, we prove that there is no near-extremal Type I [24m,12m,2m+2] binary self-dual code with minimal shadow if m≥323, and we prove that there is no near-extremal Type I (6m+1,26m+1,2m+1) additive self-dual code over GF(4) with minimal shadow if m≥22.

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Karadeniz, Suat, Bahattin Yildiz, and Nuh Aydin. "Extremal binary self-dual codes of lengths 64 and 66 from four-circulant constructions over F2+uF2." Filomat 28, no. 5 (2014): 937–45. http://dx.doi.org/10.2298/fil1405937k.

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A classification of all four-circulant extremal codes of length 32 over F2 + uF2 is done by using four-circulant binary self-dual codes of length 32 of minimum weights 6 and 8. As Gray images of these codes, a substantial number of extremal binary self-dual codes of length 64 are obtained. In particular a new code with ?=80 in W64,2 is found. Then applying an extension method from the literature to extremal self-dual codes of length 64, we have found many extremal binary self-dual codes of length 66. Among those, five of them are new codes in the sense that codes with these weight enumerators

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Pender, Thomas. "On extremal and near-extremal self-dual ternary codes." Discrete Mathematics 347, no. 6 (2024): 113968. http://dx.doi.org/10.1016/j.disc.2024.113968.

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GABORIT, PHILIPPE, ANN MARIE NATIVIDAD, and PATRICK SOLÉ. "EISENSTEIN LATTICES, GALOIS RINGS AND QUATERNARY CODES." International Journal of Number Theory 02, no. 02 (2006): 289–303. http://dx.doi.org/10.1142/s1793042106000577.

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Self-dual codes over the Galois ring GR(4,2) are investigated. Of special interest are quadratic double circulant codes. Euclidean self-dual (Type II) codes yield self-dual (Type II) ℤ4-codes by projection on a trace orthogonal basis. Hermitian self-dual codes also give self-dual ℤ4-codes by the cubic construction, as well as Eisenstein lattices by Construction A. Applying a suitable Gray map to self-dual codes over the ring gives formally self-dual 𝔽4-codes, most notably in length 12 and 24. Extremal unimodular lattices in dimension 38, 42 and the first extremal 3-modular lattice in dimension

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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 (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 (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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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 abou

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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<br>東吳大學<br>數學系<br>93<br>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<br>東吳大學<br>數學系<br>91<br>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

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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<br>東吳大學<br>數學系<br>85<br>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)

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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<br>國立成功大學<br>數學系應用數學碩博士班<br>92<br>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. 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. 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. 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. 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 coi

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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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