On Skew Cyclic Codes over a Finite Ring
Authors
Abstract:
In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.
similar resources
Skew Generalized Quasi-Cyclic Codes Over Finite Fields
In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...
full textA Note on The Enumeration of Euclidean Self-Dual Skew-Cyclic Codes over Finite Fields
In this paper, we give the enumeration formulas for Euclidean selfdual skew-cyclic codes over finite fields when (n, |θ|) = 1 and for some cases when (n, |θ|) > 1, where n is the length of the code and |θ| is the order of automorphism θ.
full textSkew constacyclic codes over finite chain rings
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right divisors of x − λ, where λ is a unit element, are exhibited. When λ = 1, the generators of Euclidean and Hermitian dual codes of such codes are determined tog...
full textCyclic codes over finite rings
It is well known that cyclic linear codes of length n over a (finite) field F can be characterized in terms of the factors of the polynomial x"-1 in F[x]. This paper investigates cyclic linear codes over arbitrary (not necessarily commutative) finite tings and proves the above characterization to be true for a large class of such codes over these rings. (~) 1997 Elsevier Science B.V. All rights...
full textOn skew cyclic codes over $F_q+vF_q+v^2F_q$
In the present paper, we study skew cyclic codes over the ring $F_{q}+vF_{q}+v^2F_{q}$, where $v^3=v,~q=p^m$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $F_{q}+vF_{q}+v^2F_{q}$ using decomposition method. By defining a Gray map from $F_{q}+vF_{q}+v^2F_{q}$ to $F_{q}^3$, it has been proved that the Gray image of a skew cyclic code of length $n$ ove...
full textOn the Codes over a Semilocal Finite Ring
In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. The Gray images of cyclic, quasi cyclic, skew cyclic, skew quasi cyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error corr...
full textMy Resources
Journal title
volume 14 issue 1
pages 135- 145
publication date 2019-04
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023