# On cyclic DNA codes over the rings Z_{4}+wZ_{4} and Z_{4}+wZ_{4}+vZ_{4}+wvZ_{4}

@article{Dertli2016OnCD, title={On cyclic DNA codes over the rings Z\_\{4\}+wZ\_\{4\} and Z\_\{4\}+wZ\_\{4\}+vZ\_\{4\}+wvZ\_\{4\}}, author={Abdullah Dertli and Yasemin Cengellenmis}, journal={ArXiv}, year={2016}, volume={abs/1605.02968} }

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 established, respectively. Cyclic codes of odd length over the finite ring R satisfies reverse complement constraint and cyclic codes of odd length over the finite ring S satisfy reverse constraint and reverse complement constraint are studied. Binary images…

## 5 Citations

On the Skew Cyclic Codes and the Reversibility Problem for DNA 4-Bases

- Mathematics, Computer ScienceMath. Comput. Sci.
- 2020

The reversible DNA codes are obtained, by using the skew cyclic codes whose generator polynomials satisfy some conditions, and the reversibility problem for DNA 4-bases can be solved.

On DNA Codes using the Ring Z4 + wZ4

- Computer Science2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

This work establishes a one to one correspondence, between the elements of the ring $R$ and all the DNA words of length 2, by defining a distance preserving Gau map $\phi$.

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

- Computer ScienceJournal of Algebra Combinatorics Discrete Structures and Applications
- 2021

The reversibility problem for DNA 4-bases is solved and the skew cyclic codes are used to construct reversible DNA codes.

Reversible complement cyclic codes over Galois rings with application to DNA codes

- Computer ScienceDiscret. Appl. Math.
- 2020

The Art of DNA Strings: Sixteen Years of DNA Coding Theory

- Computer ScienceArXiv
- 2016

This work surveys this interesting area of DNA coding theory by providing key ideas of the area and current known results.

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