In this paper convolutional codes with cyclic structure will be investigated. These codes can be understood as left principal ideals in a suitable skew-polynomial ring. It has been shown in [3] that only certain combinations of the parameters (field size, length, dimension, and Forney indices) can occur for cyclic codes. We will investigate whether all these combinations can indeed be realized ...

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...

In analogy to cyclic codes, we study linear codes over finite fields obtained from left ideals in a quotient ring of a (non commutative) skew polynomial ring. The paper shows how existence and properties of such codes are linked to arithmetic properties of skew polynomials. This class of codes is a generalization of the θ-cyclic codes discussed in [1]. However θ-cyclic codes are performant repr...

This article discusses skew generalized quasi-cyclic codes over any finite field F with Galois automorphism θ. This is a generalization of quasi-cyclic codes and skew polynomial codes. These codes have an added advantage over quasi-cyclic codes since their lengths do not have to be multiples of the index. After a brief description of the skew polynomial ring F[x; θ], we show that a skew general...

In this work, cyclic-skew-cyclic codes and sum-rank BCH are introduced. Cyclic-skew-cyclic characterized as left ideals of a suitable non-commutative finite ring, constructed using skew polynomials on top (or vice versa). Single generators such found, they used to construct generator matrices the corresponding codes. The notion defining set is introduced, pairs roots poynomials. A lower bound (...

for a finite field $mathbb{f}_q$, the bivariate skew polynomial ring $mathbb{f}_q[x,y;rho,theta]$ has been used to study codes cite{xh}. in this paper, we give some characterizations of the ring $r[x,y;rho,theta]$, where $r$ is a commutative ring. we investigate 2-d skew $(lambda_1,lambda_2)$-constacyclic codes in the ring $r[x,y;rho,theta]/langle x^l-lambda_1,y^s-lambda_2rangle_{mathit{l}}.$ a...

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...

In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R = Z3+vZ3+v 2 Z3, v 3 = v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasicyclic 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 paramete...

In this paper, we study skew cyclic codes with arbitrary length over the ring $R=\mathbb{F}_{p}+u\mathbb{F}_{p}$ where $p$ is an odd prime and $% u^{2}=0$. We characterize all skew cyclic codes of length $n$ as left $% R[x;\theta ]$-submodules of $R_{n}=R[x;\theta ]/\langle x^{n}-1\rangle $. We find all generator polynomials for these codes and describe their minimal spanning sets. Moreover, an...