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CONSTRUCTION OF DNA CODES USING $\theta$-SKEW CYCLIC CODES OVER $\mathbb{F}_4+v \mathbb{F}_4$
Keywords:
θ-skew cyclic codes, non-chain rings, Gray map, reversible codes, DNA codes.DOI:
https://doi.org/10.17654/0974165825047Abstract
In this paper, we determine the structure of $\theta$-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 $\mathbb{F}_4+v \mathbb{F}_4$. Using a correspondence between $R$ and DNA 2-bases, we characterize $\theta$-skew cyclic reversible DNA codes and $\theta$-skew cyclic reversible-complement DNA codes over this ring. We also derive the Gray images of $\theta$-skew cyclic codes.
Received: June 17, 2025
Revised: August 17, 2025
Accepted: September 12, 2025
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