DNA codes from skew dihedral group ring

Abstract

<p style='text-indent:20px;'>In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing this matrix construction, the ring <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{F}_{j, k} $\end{document}</tex-math></inline-formula> and its associated Gray maps, we show how one can construct reversible codes of length <inline-formula><tex-math id="M2">\begin{document}$ n2^{j+k} $\end{document}</tex-math></inline-formula> over the finite field <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_4. $\end{document}</tex-math></inline-formula> 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.</p>