Construction of DNA codes using $\theta$-skew cyclic codes over ${\mathbb{F}}_4+v{\mathbb{F}}_4$

Abstract

In this paper, we investigate $\theta$-skew cyclic codes over the ring $R={\mathbb{F}}_4+v{\mathbb{F}}_4$, where $v^2=v$ and $\theta$ is a non-trivial automorphism over ${\mathbb{F}}_4+v{\mathbb{F}}_4$. This allows us to describe DNA code over this ring by characterizing $\theta$-skew cyclic reversible DNA codes and $\theta$-skew cyclic reversible complement DNA codes. We also explore the Gray images of $\theta$-skew cyclic codes.