Related papers: On Quantum Codes Obtained From Cyclic Codes Over F…

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…

We first define a new Gray map from $R=\mathbb{Z}_4+u\mathbb{Z}_4$ to $\mathbb{Z}^{2}_{4}$, where $u^2=1$ and study $(1+2u)$-constacyclic codes over $R$. Also of interest are some properties of $(1+2u)$-constacyclic codes over $R$.…

In this paper quadratic residue codes over the ring Fp + vFp are introduced in terms of their idempotent generators. The structure of these codes is studied and it is observed that these codes share similar properties with quadratic residue…

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…

We study the structure of linear codes over the ring $B_k$ which is defined by $\mathbb{F}_{p^r}[v_1,v_2,\ldots,v_k]/\langle v_i^2=v_i,~v_iv_j=v_jv_i \rangle_{i,j=1}^k.$ In order to study the codes, we begin with studying the structure of…

Let $ \mathbb F_2[u]/ \langle u^k \rangle= \mathbb F_2+u\mathbb F_2+u^2\mathbb F_2+\cdots+u^{k-1}\mathbb F_2 ,$ where $u^k=0$ for a positive integer $k$, and $\mathcal{R}=M_4 (\mathbb F_2( u)/ \langle u^k \rangle)$ be the finite…

In this paper, we mainly study the some structure of cyclic DNA codes of odd length over the ring $R = \F_2[u,v]/\langle u^2-1,v^3-v,uv-vu \rangle$ which play an important role in DNA computing. We established a direct link between the…

In this work, extension theorems are generalized to self-dual codes over rings and as applications many new binary self-dual extremal codes are found from self-dual codes over F_2^m+uF_2^m for m = 1, 2. The duality and distance preserving…

Let $\mathbb{F}_{q}$ be the finite field with $q$ elements. This paper mainly researches the polynomial representation of double cyclic codes over $\mathbb{F}_{q}+v\mathbb{F}_{q}+v^2\mathbb{F}_{q}$ with $v^3=v$. Firstly, we give the…

Linear codes are considered over the ring $\mathbb{Z}_4+v\mathbb{Z}_4$, where $v^2=v$. Gray weight, Gray maps for linear codes are defined and MacWilliams identity for the Gray weight enumerator is given. Self-dual codes, construction of…

Let $m\geq 2$ be any natural number and let $\mathcal{R}=\mathbb{F}_{p}+u\mathbb{F}_{p}+u^2\mathbb{F}_{p}+\cdots+u^{m-1}\mathbb{F}_{p}$ be a finite non-chain ring, where $u^m=u$ and $p$ is a prime congruent to $1$ modulo $(m-1)$. In this…

In this paper, we mainly study the theory of linear codes over the ring $R =\mathbb{Z}_4+u\mathbb{Z}_4+v\mathbb{Z}_4+uv\mathbb{Z}_4$. By the Chinese Remainder Theorem, we have $R$ is isomorphic to the direct sum of four rings…

Let $F_p$ be the prime field with $p$ elements. We derive the homogeneous weight on the Frobenius matrix ring $M_2(F_p)$ in terms of the generating character. We also give a generalization of the Lee weight on the finite chain ring…

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,…

Due to their rich algebraic structure, cyclic codes have a great deal of significance amongst linear codes. Duadic codes are the generalization of the quadratic residue codes, a special case of cyclic codes. The $m$-adic residue codes are…

Generalized quasi-cyclic (GQC) codes with arbitrary lengths over the ring $\mathbb{F}_{q}+u\mathbb{F}_{q}$, where $u^2=0$, $q=p^n$, $n$ a positive integer and $p$ a prime number, are investigated. By the Chinese Remainder Theorem,…

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…

Classes of self-dual codes and dual-containing codes are constructed. The codes are obtained within group rings and, using an isomorphism between group rings and matrices, equivalent codes are obtained in matrix form. Distances and other…

Cyclic codes over R have been introduced recently. In this paper, we study the cyclic codes over R and their $\Z_2$ image. Making use of algebraic structure, we find the some good $\Z_2$ codes of length 28.

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…