Results 41 to 50 of about 1,045 (128)
On the codes over the Z_3+vZ_3+v^2Z_3
, 2015 In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R=Z_3+vZ_3+v^2Z_3, v^3=v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasi-cyclic and skew constacyclic codes over
Cengellenmis, Yasein +2 more
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Finite Fields and Their Applications, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Linear Algebra and its Applications, 2016 In this paper we investigate the class of constacyclic codes, which is a natural generalization of the class of cyclic and negacyclic codes. This class of codes is interesting in the sense that it contains codes with good or even optimal parameters.
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An overview on skew constacyclic codes and their subclass of LCD codes
Advances in Mathematics of Communications, 2021 Linear complementary dual (LCD) codes were introduced by Massey in 1994 [\textit{X. Yang} and \textit{J. L. Massey}, Discrete Math. 126, No. 1--3, 391--393 (1994; Zbl 0790.94022)] and proved that asymptotically good LCD codes exists [\textit{J. L. Massey}, Discrete Math. 106/107, 337--342 (1992; Zbl 0754.94009)]. From 2016 to 2018, some authors studied
Boulanouar, Ranya +2 more
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Open Mathematics, 2022 Let q=pmq={p}^{m}, pp be an odd prime, and Rk=Fq[u1,u2,ā¦,uk]/āØui3=ui,uiuj=ujuiā©{R}_{k}={{\mathbb{F}}}_{q}\left[{u}_{1},{u}_{2},\ldots ,{u}_{k}]\hspace{-0.08em}\text{/}\hspace{-0.08em}\langle {u}_{i}^{3}={u}_{i},{u}_{i}{u}_{j}={u}_{j}{u}_{i}\rangle ...
Kong Bo, Zheng Xiying
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A class of constacyclic codes are generalized ReedāSolomon codes
Designs, Codes and Cryptography, 2023 Maximum distance separable (MDS) codes are optimal in the sense that the minimum distance cannot be improved for a given length and code size. The most prominent MDS codes are generalized Reed-Solomon (GRS) codes. The square $\mathcal{C}^{2}$ of a linear code $\mathcal{C}$ is the linear code spanned by the component-wise products of every pair of ...
Hongwei Liu 0003, Shengwei Liu
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Symbol-Triple Distance of Repeated-Root Constacyclic Codes of Prime Power Lengths over
Mathematics, 2022 Let p be an odd prime, where Ļ and m are positive integers. Let Ļ be a nonzero element of the finite field Fq, where q=pm, and R=Fq+uFq+u2Fq(u3=0). In this paper, we determine completely the symbol-triple distances of all Ļ-constacyclic codes of length ...
Hai Q. Dinh +3 more
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On the equivalence of linear cyclic and constacyclic codes
Discrete Mathematics, 2023 We introduce new sufficient conditions for permutation and monomial equivalence of linear cyclic codes over various finite fields. We recall that monomial equivalence and isometric equivalence are the same relation for linear codes over finite fields.
Reza Dastbasteh, Petr Lisonek
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Mathematics, 2021 Let p be a prime, s, m be positive integers, Ī³ be a nonzero element of the finite field Fpm, and let R=Fpm[u]/āØu3ā© be the finite commutative chain ring.
Mohammed E. Charkani +3 more
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Quantum MDS Codes over Small Fields
, 2015 We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS codes can be ...
Grassl, Markus, Roetteler, Martin
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