Cyclic DNA codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_2[u,v]/\langle u^3, v^2-v, vu-uv\rangle$\end{document}</tex-math></inline-formula>

Abstract

In this paper, we construct cyclic DNA codes over the ringThe correspondence between the elements of R and the alphabet {A, T, G, C} 3 is obtained by a given Gray map. Moreover, some properties of binary images of the Condons under the Gray map are also discussed. Finally, two examples of cyclic DNA codes over R are presented to illustrate the obtained results.