Related papers: A note on the duals of skew constacyclic codes

In this article, for a finite field $\mathbb{F}_q$ and a natural number $l,$ let $\mathcal{R}$ denote the product ring $\mathbb{F}_q^l.$ Firstly, for an automorphism $\Theta$ of $\mathcal{R},$ a $\Theta$-derivation $\Delta_\Theta$ of…

Let q be a prime power and F_q be a finite field. In this paper, we study constacyclic codes over the ring F_q+ u F_q +v F_q+ u v F_q, where u^2=u, v^2=v and uv=vu. We characterized the generator polynomials of constacyclic codes and their…

For a prime $p$, let $F_q$ be the finite field of order $q= p^d$. This paper presents the study on skew generalized quasi-cyclic (SGQC) codes of length $n$ over the non-chain ring $F_q+vF_q$ where $v^2=v$ and $\theta_t$ is the Galois…

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…

Let $R^t$ denote the finite chain ring $\frac{\mathbb{F}_{p^m}[u]}{\langle u^t \rangle},$ where $p$ is a prime and $t$ is a positive integer. In this article, for a prime $p$ and an automorphism $\theta$ of $\mathbb{F}_{p^m}$, we give the…

In this paper, we study some repeated-root two-dimensional cyclic and constacyclic codes over a finite field $F=\mathbb{F}_q$. We obtain the generator matrices and generator polynomials of these codes and their duals. We also investigate…

Let $q$ be a prime power and let $\mathcal{R}=\mathbb{F}_{q}[u_1,u_2, \cdots, u_k]/\langle f_i(u_i),u_iu_j-u_ju_i\rangle$ be a finite non-chain ring, where $f_i(u_i), 1\leq i \leq k$ are polynomials, not all linear, which split into…

The aim of this paper is to give conditions for the equivalency between skew constacyclic codes, skew cyclic codes and skew negacyclic codes defined over semi-local rings. Also, we provide construction and an enumeration of Euclidean and…

In this article, we study skew cyclic codes over ring $R=\mathbb{F}_{q}+v\mathbb{F}_{q}+v^{2}\mathbb{F}_{q}$, where $q=p^{m}$, $p$ is an odd prime and $v^{3}=v$. We describe generator polynomials of skew cyclic codes over this ring and…

Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic…

In this paper we characterize the algebraic structure of two-dimensional $(\alpha,\beta )$-constacyclic codes of arbitrary length $s.\ell$ and of their duals. For $\alpha,\beta \in \{1,-1\}$, we give necessary and sufficient conditions for…

In this paper, several families of irreducible constacyclic codes over finite fields and their duals are studied. The weight distributions of these irreducible constacyclic codes and the parameters of their duals are settled. Several…

We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes…

Many kinds of codes which possess two cycle structures over two special finite commutative chain rings, such as ${\Bbb Z}_2{\Bbb Z}_4$-additive cyclic codes and quasi-cyclic codes of fractional index etc., were proved asymptotically good.…

Let $\mathbb{F}_q$ be a finite field of $q=p^m$ elements where $p$ is a prime and $m$ is a positive integer. This paper considers $(\gamma,\Delta)$-cyclic codes over a class of finite non-chain commutative rings…

In this paper we give the enumeration formulas for Euclidean self-dual skew-cyclic codes over finite fields when $(n,|\theta|)=1$ and for some cases when $(n,|\theta|)>1,$ where $n$ is the length of the code and $|\theta|$ is the order of…

We introduce an additive but not $\mathbb{F}_4$-linear map $S$ from $\mathbb{F}_4^{n}$ to $\mathbb{F}_4^{2n}$ and exhibit some of its interesting structural properties. If $C$ is a linear $[n,k,d]_4$-code, then $S(C)$ is an additive…

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…

This paper considers a new alphabet set, which is a ring that we call $\mathbb{F}_4R$, to construct linear error-control codes. Skew cyclic codes over the ring are then investigated in details. We define a nondegenerate inner product and…

In this work, we study a class of skew cyclic codes over the ring $R:=\mathbb{Z}_4+v\mathbb{Z}_4,$ where $v^2=v,$ with an automorphism $\theta$ and a derivation $\Delta_\theta,$ namely codes as modules over a skew polynomial ring…