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

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.