DNA codes from skew dihedral group ring

This is the authors' abstract. We don't add key points for this paper.

In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing this matrix construction, the ring <tex-math id="M1">{document}Fj, k{document}</tex-math> and its associated Gray maps, we show how one can construct reversible codes of length <tex-math id="M2">{document}n2ʲ⁺ᵏ{document}</tex-math> over the finite field <tex-math id="M3">{document}F₄.{document}</tex-math> As an application, we construct a number of DNA codes that satisfy the Hamming distance, the reverse, the reverse-complement, and the GC-content constraints with better parameters than some good DNA codes in the literature.