On reversible double cyclic codes over a non chain ring

Abstract

In this paper, we study double cyclic codes over a non chain ring $\mathcal{R}=\mathbb F_2+v\mathbb F_2$, $v^2=v$. We also study the necessary and sufficient conditions for double cyclic codes over $\mathcal{R}$ to be reversible double cyclic codes. Moreover, we extent this study to reversible-complement double cyclic codes and give necessary and sufficient conditions for $\mathcal{R}$-double cyclic codes to be reversible-complement $\mathcal{R}$-double cyclic codes. Further, we present some applications of these codes to DNA codes and constructed several examples of DNA codes.