Results 31 to 40 of about 2,635,004 (136)
Hermitian Self‐Orthogonal Constacyclic Codes over Finite Fields
Journal of Discrete Mathematics, Volume 2014, Issue 1, 2014., 2014 Necessary and sufficient conditions for the existence of Hermitian self‐orthogonal constacyclic codes of length n over a finite field Fq2, n coprime to q, are found. The defining sets and corresponding generator polynomials of these codes are also characterised. A formula for the number of Hermitian self‐orthogonal constacyclic codes of length n over a
Amita Sahni +2 more
wiley +1 more source
Gray Images of Constacyclic Codes Over Some Polynomial Residue Rings
پژوهشهای ریاضی, 2021 Let be the quotient ring where is the finite field of size and is a positive integer. A Gray map of length over is a special map from to ( .
Reza Sobhani
doaj
Construction of New Matrix-Product Codes and Their Applications
IEEE Access, 2019 In this paper, from special code chains $\mathcal {C}_{1} \supseteq \mathcal {C}_{2}~\supseteq \mathcal {C}_{3}$ such that $\mathcal {C}^{\bot _{h}}_{1}\subseteq \mathcal {C}_{3}$ and $\mathcal {C}^{\bot _{h}}_{2}\subseteq \mathcal {C}_{2}$ , some ...
Hao Song +3 more
doaj +1 more source
New quantum codes from skew constacyclic codes
Advances in Mathematics of Communications, 2023 In the paper under review, the authors construct quantum codes from skew constacyclic codes over the finite commutative non-chain ring of order \(p^{2^{\ell} m}\) with characteristic odd prime \(p\): \[ R_{\ell,m} = \mathbb{F}_{p^m}[v_1,v_2,\dots,v_{\ell}]/\langle v^2_i-1, v_iv_j-v_jv_i\rangle_{1\leq i, j\leq \ell}, \] where \(m\) and \(\ell\) are ...
Verma, Ram Krishna +3 more
openaire +2 more sources
On $ \sigma $-self-orthogonal constacyclic codes over $ \mathbb F_{p^m}+u\mathbb F_{p^m} $
Advances in Mathematics of Communications, 2022 In this paper, we generalize the notion of self-orthogonal codes to \begin{document}$ \sigma $\end{document} -self-orthogonal codes over an arbitrary finite ring.
Hongwei Liu, Jingge Liu
semanticscholar +1 more source
Constacyclic codes as invariant subspaces
Linear Algebra and its Applications, 2009 A constacyclic code (sometimes also referred to as pseudo-cyclic code) is a linear code over a field GF\((q)\) invariant under the permutation \(\psi_a:\) \((c_0,c_1\ldots,c_{n-1})\mapsto (ac_{n-1},c_0,c_1\ldots,c_{n-1})\) (for a fixed field element \(a\)). (In the introduction of the article the definition is not correct).
Radkova, D., van Zanten, A.J.
openaire +4 more sources
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
core +1 more source
Finite Fields and Their Applications, 2016 Cyclic codes are a well-known class of linear block codes with efficient decoding algorithms. In recent years they have been generalized to skew-constacyclic codes; such a generalization has previously been shown to be useful. We begin with a study of skew-polynomial rings so that we may examine these codes algebraically as quotient modules of non ...
Fogarty, Neville +1 more
openaire +3 more sources
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
core +1 more source
Polycyclic codes over Galois rings with applications to repeated-root constacyclic codes
, 2012 Cyclic, negacyclic and constacyclic codes are part of a larger class of codes called polycyclic codes; namely, those codes which can be viewed as ideals of a factor ring of a polynomial ring.
Lopez-Permouth, Sergio R. +3 more
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