Results 31 to 40 of about 290,159 (337)
On self-dual affine-invariant codes [PDF]
, 1993 An extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Redd-Muller code [2m, 2m-1, 2(m+1)/2] is affine-invariant and self-dual and it is the only such code for m = 3 or 5.
Levy-Dit-Vehel, Françoise +1 more
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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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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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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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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
doaj +1 more source
IEEE Access, 2023 A code over Gaussian or Eisenstein integer residue ring is an additive group of vectors with entries in this integer residue ring which is closed under the action of constant multiplication by the Gaussian or Eisenstein integers. In this paper, we define
Hajime Matsui
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Constructing self-dual codes from group rings and reverse circulant matrices
Advances in Mathematics of Communications, 2021 In this work, we describe a construction for self-dual codes in which we employ group rings and reverse circulant matrices. By applying the construction directly over different alphabets, and by employing the well known extension and neighbor methods we ...
J. Gildea, A. Korban, A. Kaya, B. Yildiz
semanticscholar +1 more source
Linear programming bounds for doubly-even self-dual codes [PDF]
, 1997 Using a variant of linear programming method we derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives d/n
Krasikov, I, Simon Litsyn, Ilia Krasikov
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An improved upper bound on the minimum distance of doubly-even self-dual codes [PDF]
, 2000 We derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives limn→∞ sup d/n
Krasikov, I, Litsyn, S
core +1 more source
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
openaire +6 more sources