On the Codes over a Family of Rings and Their Applications to DNA Codes

Authors : Abdullah DERTLİ, Yasemin CENGELLENMİS

Pages : 164-177

Doi:10.36753/mathenot.903589

View : 65 | Download : 72

Publication Date : 2023-09-02

Article Type : Research Paper

Abstract :In this paper, the structures of the linear codes over a family of the rings $A_{t}=Z_{4}\\left[ u_{1},\\ldots ,u_{t}\\right] \\left/ \\left\\langle u_{i}^{2}-u_{i},u_{i}u_{j}-u_{j}u_{i}\\right\\rangle \\right. $ are given, where $i,j=1,2,\\ldots ,t$, $i\\neq j$, $Z_{4}=\\{0,1,2,3\\}$. A map between the elements of the $A_{t}$ and the alphabet $\\left\\{ A,T,C,G\\right\\} ^{2^{t}}$ is constructed. The DNA codes are obtained with three different methods, by using the cyclic, skew cyclic codes over a family of the rings $A_{t}$ and $\\theta _{i}$-set, where $\\theta _{i}$ is a non trivial automorphism on $A_{i}$, for $i=1,2,\\ldots ,t$.
Keywords : DNA codes, Skew cyclic codes, Reversibility

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