Results 21 to 30 of about 374,835 (257)
Neighborhoods of Binary Self-Dual Codes
Contemporary Mathematics, 2023 In this paper, we introduce and investigate the neighborhood of binary self-dual codes. We prove that there is no better Type I code than the best Type II code of the same length. Further, we give some new necessary conditions for the existence of a singly-even (56,28,12)-code and a doubly-even (72,36,16)-code.
Carolin Hannusch, S. Roland Major
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Classification of quaternary Hermitian self-dual codes of length 20 [PDF]
, 2010 A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.Comment: 9 pages.
Harada, Masaaki, Munemasa, Akihiro
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SHADOW OPTIMAL SELF-DUAL CODES
Kyushu Journal of Mathematics, 1999 This paper considers binary linear self-dual codes. An optimal self-dual code has the highest minimum weight for the given length. Shadow codes were previously introduced by \textit{J. H. Conway} and \textit{N. J. A. Sloane} [IEEE Trans. Inf. Theory 36, 1319-1333 (1990; Zbl 0713.94016)].
Dougherty, Steven T., Harada, Masaaki
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Self-Dual Cyclic Codes Over M2(ℤ4)
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet.
Bhowmick Sanjit +3 more
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Quantum codes from $ \sigma $-dual-containing constacyclic codes over $ \mathfrak{R}_{l, k} $
AIMS Mathematics, 2023 Let $ \mathfrak{R}_{l, k} = {\mathbb F}_{p^m}[u_1, u_2, \cdots, u_k]/ \langle u_{i}^{l} = u_{i}, u_iu_j = u_ju_i = 0 \rangle $, where $ p $ is a prime, $ l $ is a positive integer, $ (l-1)\mid(p-1) $ and $ 1\leq i, j\leq k $. First, we define a Gray map $
Xiying Zheng, Bo Kong, Yao Yu
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Construction of isodual codes from polycirculant matrices
, 2020 Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual.
Shi, Minjia, Sole, Patrick, Xu, Li
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Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound [PDF]
, 2005 A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and ...
Stichtenoth, Henning
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On self-dual double circulant codes [PDF]
Designs, Codes and Cryptography, 2017 Self-dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta-dihedral in odd characteristic. Exact counting formulae are derived for them and used to show they contain families of codes with relative distance satisfying a modified Gilbert-Varshamov bound.
Alahmadi, Adel +2 more
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Reversible Self-Dual Codes Over the Ring F2 +
IEEE AccessIn this study, we introduce bisymmetric self-dual codes over the finite field ${\mathbb F}_{2}$ of order two. We developed a method to generate binary bisymmetric self-dual codes from a small-length bisymmetric self-dual code by increasing its length ...
Hyun Jin Kim, Whan-Hyuk Choi
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Triorthogonal codes and self-dual codes
Quantum Information Processing21 ...
Shi, Minjia +3 more
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