On the Codes Over the Ring Z4 + uZ4 + vZ4 Cyclic, Constacyclic, Quasi-Cyclic Codes, Their Skew Codes, Cyclic DNA & Skew Cyclic DNA Codes

Abstract

In the paper, the linear codes over the ring Z₄ + uZ₄ + vZ₄ are studied. The Gray images of the cyclic, constacyclic and quasi-cyclic codes over are determined. Especially, cyclic DNA codes over are introduced. A nontrivial automorphism is given. The skew cyclic, constacyclic and quasi-cyclic are introduced. The Gray images of them are determined. Furthermore, the skew cyclic DNA codes over are introduced.