Related papers: Construction of $(\sigma,\delta)$-cyclic codes ove…
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…
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…
This paper is dealing with DNA cyclic codes which play an important role in DNA computing and have attracted a particular attention in the literature. Firstly, we introduce a new family of DNA cyclic codes over the ring…
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 paper, we solve the reversibility problem for DNA codes over the non-chain ring $R_{k,s}=\mathbb{F}_{4^{2k}}[u_1,...,u_{s}]/< u_1^2-u_1,..., u_s^2-u_s>$. We define an automorphism $\theta$ over $R_{k,s}$ which help us both find the…
We construct codes over the ring $\mathbb{F}_2+u\mathbb{F}_2$ with $u^2=0$. These code are designed for use in DNA computing applications. The codes obtained satisfy the reverse complement constraint, the $GC$ content constraint and avoid…
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…
In this article, we study the algebraic structure of double cyclic codes of length $(m, n)$ over $\mathbb{F}_4$ and we give a necessary and sufficient condition for a double cyclic code over $\mathbb{F}_4$ to be reversible. Also, we…
In this work, we study the structure of cyclic DNA codes of arbitrary lengths over the ring R=F2+uF2+vF2+uvF2 and establish relations to codes over R1=F2+uF2 by defining a Gray map between R and R1^2 where R1 is the ring with 4 elements.…
In this paper, we study the theory for constructing DNA cyclic codes of odd length over $\Z_4[u]/\langle u^2 \rangle$ which play an important role in DNA computing. Cyclic codes of odd length over $\Z_4 + u \Z_4$ satisfy the reverse…
This work introduces a novel approach to constructing DNA codes from linear codes over a non-chain extension of $\mathbb{Z}_4$. We study $(\text{\textbaro},\mathfrak{d}, \gamma)$-constacyclic codes over the 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…
This paper considers cyclic DNA codes of arbitrary length over the ring $R=\F_2[u]/u^4-1$. A mapping is given between the elements of $R$ and the alphabet $\{A,C,G,T\}$ which allows the additive stem distance to be extended to this ring.…
The structures of cyclic DNA codes of odd length over the finite rings R=Z_{4}+wZ_{4}, w^{2}=2 and S=Z_{4}+wZ_{4}+vZ_{4}+wvZ_{4},w^{2}=2,v^{2}=v,wv=vw are studied. The links between the elements of the rings R, S and 16 and 256 codons are…
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…
In this paper, we discuss DNA codes that are cyclic or quasi-cyclic over $\Z_{4}+\omega \Z_{4}$, where $\omega^{2}=2+2\omega$ along with methods to construct these with combinatorial constraints. We also generalize results obtained for the…
In this study we determine the structure of reversible DNA codes obtained from skew cyclic codes. We show that the generators of such DNA codes enjoy some special properties. We study the structural properties of such family of codes and we…
Let $A$ be a ring with identity, $\sigma$ a ring endomorphism of $A$ that maps the identity to itself, $\delta$ a $\sigma$-derivation of $A$, and consider the skew-polynomial ring $A[X;\sigma,\delta]$. When $A$ is a finite field, a Galois…
In the present paper we study the structure of cyclic DNA codes of even lenght over the ring $\mathbb{F}_2+u\mathbb{F}_2+u^2\mathbb{F}_2$ where $u^3=0$. We investigate two presentations of cyclic codes of even lenght over…
In this paper we study the structure of specific linear codes called DNA codes. The first attempts on studying such codes have been proposed over four element rings which are naturally matched with DNA four letters. Later, double (pair) DNA…