DNA codes from skew dihedral group ring

<p style='text-indent:20px;'>In this work, we present a matrix construction for reversible codes derived from skew dihedral group rings. By employing construction, the ring <inline-formula><tex-math id="M1">\begin{document}$ \mathcal{F}_{j, k} $\end{document}</tex-math></inline-formula> and its associated Gray maps, show how one can construct of length id="M2">\begin{document}$ n2^{j+k} over finite field id="M3">\begin{document}$ \mathbb{F}_4. As an application, number DNA that satisfy Hamming distance, reverse, reverse-complement, GC-content constraints with better parameters than some good in literature.</p>