Results 11 to 20 of about 645,715 (278)
On Self-Dual Four Circulant Codes [PDF]
International Journal of Foundations of Computer Science, 2018 Four circulant codes form a special class of [Formula: see text]-generator, index [Formula: see text], quasi-cyclic codes. Under some conditions on their generator matrix they can be shown to be self-dual. Artin primitive root conjecture shows the existence of an infinite subclass of these codes satisfying a modified Gilbert–Varshamov bound.
Minjia Shi +3 more
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Galois self-dual constacyclic codes [PDF]
Designs, Codes and Cryptography, 2016 Key words: Constacyclic code, Galois inner product, $q$-coset function, isometry, Galois self-dual ...
Yun Fan, Liang Zhang
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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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Advances in Mathematics of Communications, 2016 Improved exposition according to the referees ...
Gabriele Nebe, Wolfgang Willems
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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.
Adel Alahmadi +2 more
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established ...
Castillo-Guillén C. A. +1 more
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Self-Dual and Complementary Dual Abelian Codes over Galois Rings [PDF]
, 2019 Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications.
Jitman, Somphong, Ling, San
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On the enumeration of self-dual codes
Journal of Combinatorial Theory, Series A, 1980 AbstractWe give the complete classification of all binary, self-dual, doubly-even (32, 16) codes. There are 85 non-equivalent, self-dual, doubly-even (32, 16) codes. Five of these have minimum weight 8, namely, a quadratic residue code and a Reed-Muller code, and three new codes.
John H. Conway, Vera Pless
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Narain CFTs and error-correcting codes on finite fields
Journal of High Energy Physics, 2022 We construct Narain CFTs from self-dual codes on the finite field F p through even self-dual lattices for any prime p > 2. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error correction capability ...
Shinichiro Yahagi
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Group rings, G-codes and constructions of self-dual and formally self-dual codes [PDF]
Designs, Codes and Cryptography, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Steven T. Dougherty +3 more
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