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

TL;DR

This paper investigates the structure and properties of cyclic DNA codes over specific finite rings, establishing their relations to codons and constructing skew cyclic codes with reverse complement properties.

Contribution

It introduces new cyclic DNA code constructions over rings R and S, analyzing their constraints and binary images, and develops a family of DNA skew cyclic codes with reverse complement features.

Findings

Cyclic DNA codes over R satisfy reverse complement constraint.

Cyclic DNA codes over S satisfy reverse and reverse complement constraints.

Binary images of these codes are explicitly determined.

Abstract

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 of the cyclic DNA codes over the finite rings R and S are determined. Moreover, a family of DNA skew cyclic codes over R is constructed, its property of being reverse complement is studied.