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

TL;DR

This paper develops a new class of DNA codes using $ heta$-skew cyclic codes over a specific ring, enabling the construction of reversible and complement DNA codes with potential applications in DNA computing.

Contribution

It introduces $ heta$-skew cyclic codes over the ring $ ext{F}_4 + v ext{F}_4$ and characterizes their properties for DNA code construction, including reversibility and complementarity.

Findings

Characterization of $ heta$-skew cyclic reversible DNA codes.

Construction of $ heta$-skew cyclic reversible complement DNA codes.

Analysis of Gray images of these codes.

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.