TY  - JOUR
T1  - On the Codes over a Family of Rings and Their Applications to DNA Codes
AU  - Dertli, Abdullah
AU  - Cengellenmis, Yasemin
PY  - 2023
DA  - September
Y2  - 2022
DO  - 10.36753/mathenot.903589
JF  - Mathematical Sciences and Applications E-Notes
JO  - Math. Sci. Appl. E-Notes
PB  - Murat TOSUN
WT  - DergiPark
SN  - 2147-6268
SP  - 164
EP  - 177
VL  - 11
IS  - 3
LA  - en
AB  - 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 $i=1,2,\ldots ,t$.
KW  - DNA codes
KW  - Skew cyclic codes
KW  - Reversibility
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UR  - https://doi.org/10.36753/mathenot.903589
L1  - https://dergipark.org.tr/en/download/article-file/1663480
ER  -