相关论文: On skew cyclic codes over $F_q+vF_q+v^2F_q$

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…

In this note, we study skew cyclic and skew constacyclic codes over the ring $\mathcal{R}=F_{q}+uF_{q}+vF_{q}+uvF_{q}$ where $q=p^{m},$ $p$ is an odd prime, $u^{2}=u,~v^{2}=v,~uv=vu$. We show that Gray images of a skew cyclic and skew…

In this paper, we study skew cyclic codes over the ring $R=\F_q+u\F_q+v\F_q+uv\F_q$, where $u^{2}=u,v^{2}=v,uv=vu$, $q=p^{m}$ and $p$ is an odd prime. We investigate the structural properties of skew cyclic codes over $R$ through a…

In this paper skew constacyclic codes over finite non-chain ring R = F_q+uF_q+vF_q, where q= p^m, p is an odd prime and u^{2}=u, v^{2}=v, uv = vu = 0 are studied. We show that Gray image of a skew alpha-constacyclic cyclic code of length n…

Let $p$ be a prime and $\mathbb{F}_q$ be the finite field of order $q=p^m$. In this paper, we study $\mathbb{F}_q\mathcal{R}$-skew cyclic codes where $\mathcal{R}=\mathbb{F}_q+u\mathbb{F}_q$ with $u^2=u$. To characterize…

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…

In this study, in order to get better codes, we focus on double skew cyclic codes over the ring $\mathrm{R}= \mathbb{F}_q+v\mathbb{F}_q, ~v^2=v$ where $q$ is a prime power. We investigate the generator polynomials, minimal spanning sets,…

In this paper, the investigation on the algebraic structure of the ring $\frac{\mathbb{F}_q[v]}{\langle\,v^q-v\,\rangle}$ and the description of its automorphism group, enable to study the algebraic structure of codes and their dual over…

In this article, we study the skew cyclic codes over R_{k}=F_{p}+uF_{p}+\dots +u^{k-1}F_{p} of length n. We characterize the skew cyclic codes of length $n$ over R_{k} as free left R_{k}[x;\theta]-submodules of R_{k}[x;\theta]/\langle…

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…

In this paper, we give conditions for the existence of Hermitian self-dual $\Theta-$cyclic and $\Theta-$negacyclic codes over the finite chain ring $\mathbb{F}_q+u\mathbb{F}_q$. By defining a Gray map from $R=\mathbb{F}_q+u\mathbb{F}_q$ to…

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…

In this paper, we investigate cyclic code over the ring $\mathbb{F}_{p^k} + v\mathbb{F}_{p^k} + v^2\mathbb{F}_{p^k} + ... + v^r\mathbb{F}_{p^k}$, where $v^{r+1}=v$, $p$ a prime number, $r>1$ and $\gcd(r,p)=1$, we prove as generalisation of…

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…

In this article, we investigate properties of cyclic codes over a finite non-chain ring $\mathbb{F}_q+v\mathbb{F}_q+v^2\mathbb{F}_q+v^3\mathbb{F}_q+v^4\mathbb{F}_q,$ where $q=p^r,$ $r$ is a positive integer, $p$ is an odd prime, $4 \mid…

A new Gray map which is both an isometry and a weight preserving map from R=F_2+vF_2+v^2F_2 to (F_2)^3 is defined. A construction for quantum error correcting codes from cyclic codes over finite ring R=F_2+vF_2+v^2F_2, v^3=v is given. The…

In this paper, we investigate $\theta$-skew cyclic codes over the ring $R= \mathbb{F}_4 + v \mathbb{F}_4$, where $v^2=v$ and $\theta$ is a non-trivial automorphism over $\mathbb{F}_4 + v \mathbb{F}_4$. This allows us to describe DNA code…

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 article, we construct new non-binary quantum codes from skew constacyclic codes over finite commutative non-chain ring $\mathcal{R}= \mathbb{F}_{p^m}[v]/\langle v^3 =v \rangle$ where $p$ is an odd prime and $m \geq 1$. In order to…

We study cyclic codes with arbitrary length over Fp+vFp where theta(v)=av, a in Fp and v^2=0. We characterize all existing codes in case of O(theta)|n by using certain projections from (Fp+vFp)[x;theta] to Fp[x]. We provide an explicit…