Construction of Cyclic DNA Codes Over the Ring Z<sub>4</sub> &x002B; <italic>v</italic>Z<sub>4</sub>

In this work, we investigate DNA codes of odd length over the finite ring . Firstly, we give a map from to . Then cyclic codes of odd length satisfying the reverse and reverse-complement constraint are characterized over such ring. Moreover, when is a reverse-complement cyclic code over , we prove that 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 content of code over finite ring by means of the Gray images of the minimal generating set of .