Construction of Cyclic DNA Codes Over the Ring Z4 + vZ4

In this work, we investigate DNA codes of odd length over the finite ring $R=\mathbb {Z}_{4}+v \mathbb {Z}_{4},v^{2}=v$ . Firstly, we give a map $\Phi $ from $R^{n}$ to $\{A, T, G,C\}^{2n}$ . Then cyclic codes of odd length satisfying the reverse and reverse-complement constraint are characterized over such ring. Moreover, when $C$ is a reverse-complement cyclic code over $R$ , we prove that $\Phi (C)$ is a cyclic DNA code by using the method different from all the previously known ones, which helps us finding a new DNA code with 256 codewords. Finally, we consider the $GC$ content of code $C$ over finite ring $\mathbb {Z}_{4} + v \mathbb {Z}_{4}$ by means of the Gray images of the minimal generating set of $C$ .