@article{article_903589, title={On the Codes over a Family of Rings and Their Applications to DNA Codes}, journal={Mathematical Sciences and Applications E-Notes}, volume={11}, pages={164–177}, year={2023}, DOI={10.36753/mathenot.903589}, author={Dertli, Abdullah and Cengellenmis, Yasemin}, keywords={DNA codes, Skew cyclic codes, Reversibility}, 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 $i=1,2,\ldots ,t$.}, number={3}, publisher={Murat TOSUN}