Reversible DNA codes from skew cyclic codes over a ring of order 256

We introduce skew cyclic codes over the finite ring $\R$, where $u^{2}=0,v^{2}=v,w^{2}=w,uv=vu,uw=wu,vw=wv$ and use them to construct reversible DNA codes. The 4-mers are matched with the elements of this ring. The reversibility problem for DNA 4-bases is solved and some examples are provided

On Linear Codes Over a Non-Chain Ring

In this paper, we study skew cyclic and quasi cyclic codes over the ring S = F2 +uF2 + vF2 where u2 = u, v2 = v, uv = vu = 0.We investigate the structural properties of them. Using a Gray map on S we obtain the MacWilliams identities for codes over S. The relationships between Symmetrized, Lee and Hamming weight enumerator are determined

Codes over rings about a particular type

Bu çalışma üç bölümden oluşmaktadır. I.Bölümde kodlarla ilgili gerekli ön bilgiler verilmiştir. II.Bölümde skew cyclic kodlar, skew quasi-cyclic kodlar ve skew constacyclic kodlarla ilgili çalışmalar incelenmiştir. III.Bölümde, u_1^2=1, u_2^2=1, u_1 u_2=u_2 u_1 olmak üzere M_2=IF_2+u_1 IF_2+u_2 IF_2+u_1 u_2 IF_2 halkası üzerinde tanımlı kodlar incelenmiş ve bu halka üzerinde Gray dönüşümleri ve Lee ağırlık dönüşümü tanımlanmıştır. Ayrıca M _2 halkası üzerinde aşikar olmayan bir otomorfizması tanımlanarak, M _2 [x,?] skew polinom halkası oluşturulmuştur.AbstractThe study consists of three chapters. In Chapter I, the pertinent backround material about the codes are given. In Chapter II, the works about the skew cyclic codes, the skew quasi-cyclic codes and the skew consta cyclic codes are investigated. In Chapter III, the codes over the ring M _2=IF_2+u_1 IF_2+u_2 IF_2+u_1 u_2 IF_2 where u_1^2=1, u_2^2=1, u_1 u_2=u_2 u_1 are determined. The Gray maps and Lee weight over the ring are defined. By defining a non trivial automorphism over the ring M_2, the skew polynomial ring M_2 [x,?] is constructed

On cyclic DNA codes over the rings Z4 + wZ4 and Z4 + wZ4 + vZ4 + wvZ4

The structures of cyclic DNA codes of odd length over the finite rings R = Z4 + wZ4, w^2 = 2 and S = Z4 + wZ4 + vZ4 + wvZ4; 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 established, respectively. The cyclic codes of odd length over the finite ring R satisfy reverse complement constraint and the cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. The binary images of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied

On gray images of constacyclic codes over the finite ring F₂ + u₁F₂ + u₂F₂

We introduce the finite ring F₂ + u₁F₂ + u₂F₂, u₁ ² = u₁ , u₂ ² = 0 , u₁.u₂ = u₂.u₁ = 0 which is not a finite chain ring. We focus on (1 + u₂) -constacyclic codes over F₂ + u₁F₂ + u₂F₂ of odd length. We prove that the Gray image of a linear (1 + u₂) -constacyclic code over F₂ + u₁F₂ + u₂F₂ of odd length n is a quasi-cyclic code of index 4 and length 4n over F₂.Publisher's Versio