Cyclic codes over $${\mathbb {F}}_2 +u{\mathbb {F}}_2+v{\mathbb {F}}_2 +v^2 {\mathbb {F}}_2 $$ with respect to the homogeneous weight and their applications to DNA codes

Abstract

In this paper, we study cyclic codes and their duals over the local Frobenius non-chain ring $$R={\mathbb {F}}_2[u,v] / \langle u^2=v^2,uv \rangle $$, and we obtain optimal binary linear codes with respect to the homogeneous weight over R via a Gray map. Moreover, we characterize DNA codes as images of cyclic codes over R.