Extremal Binary and Ternary Codes of Length 60 with an Automorphism of Order 29 and a Generalization
Mathematics, 2022 In this paper, all extremal Type I and Type III codes of length 60 with an automorphism of order 29 are classified up to equivalence. In both cases, it has been proven that there are three inequivalent codes.
Stefka Bouyuklieva +2 more
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The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring
AIMS Mathematics, 2023 In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd prime ...
Adel Alahmadi, Altaf Alshuhail, P. Solé
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On Reversibility and Self-Duality for Some Classes of Quasi-Cyclic Codes
IEEE Access, 2020 In this work, we study two classes of quasi-cyclic (QC) codes and examine how several properties can be combined into the codes of these classes. We start with the class of QC codes generated by diagonal generator polynomial matrices; a QC code in this ...
Ramy Taki Eldin, Hajime Matsui
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Binary self-dual codes of various lengths with new weight enumerators from a modified bordered construction and neighbours [PDF]
Advances in Mathematics of Communications, 2021 In this work, we define a modification of a bordered construction for self-dual codes which utilises \begin{document}$ \lambda $\end{document}-circulant matrices.
J. Gildea +3 more
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Group matrix ring codes and constructions of self-dual codes [PDF]
Applicable Algebra in Engineering, Communication and Computing, 2021 In this work, we study codes generated by elements that come from group matrix rings. We present a matrix construction which we use to generate codes in two different ambient spaces: the matrix ring $$M_k(R)$$ M k ( R ) and the ring R , where R is the ...
S. Dougherty +3 more
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New binary self-dual codes of lengths 56, 58, 64, 80 and 92 from a modification of the four circulant construction [PDF]
Finite Fields Their Appl., 2021 In this work, we give a new technique for constructing self-dual codes over commutative Frobenius rings using λ-circulant matrices. The new construction was derived as a modification of the well-known four circulant construction of self-dual codes ...
J. Gildea, A. Korban, A. Roberts
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An explicit construction of quantum codes from one-generator generalized quasi-cyclic codes [PDF]
MATEC Web of Conferences, 2021 In this paper, we take advantage of a class of one-generator generalized quasi-cyclic (GQC) codes of index 2 to construct quantum error-correcting codes.
Yao Yu, Ma Yuena, Li Husheng, Lv Jingjie
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New binary self-dual codes of lengths 80, 84 and 96 from composite matrices [PDF]
Designs, Codes and Cryptography, 2021 In this work, we apply the idea of composite matrices arising from group rings to derive a number of different techniques for constructing self-dual codes over finite commutative Frobenius rings.
J. Gildea, A. Korban, A. Roberts
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Duality of Codes Over Non-Unital Rings of Order Four
IEEE Access, 2023 In this paper, we present a basic theory of the duality of linear codes over three of the non-unital rings of order four; namely $I$ , $E$ , and $H$ as denoted in (Fine, 1993).
Adel Alahmadi +2 more
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New binary self-dual codes of lengths 56, 62, 78, 92 and 94 from a bordered construction [PDF]
Discrete Mathematics, 2021 In this paper, we present a new bordered construction for self-dual codes which employs $\lambda$-circulant matrices. We give the necessary conditions for our construction to produce self-dual codes over a finite commutative Frobenius ring of ...
J. Gildea +3 more
semanticscholar +1 more source