A study of reversible DNA cyclic codes over a non-chain ring based on the deletion distance

Let R = Z8[u]/?u2 ? 4, 2u? be a non-chain ring of characteristic 8. In this article, DNA codes of odd lengths over the ring R based on the deletion distance are discussed. For this purpose, we study cyclic codes of any odd length over the ring R satisfying the reversible and the reversible complement constraints. Also, a bijection ? between the elements of the ring R and SD16 is constructed in such a way that the reversibility problem is solved. Moreover, we introduce a homogeneous weight whom over the ring R and by utilizing whom, a new Gray map ?hom : Rn ? F8n 2 is obtained. Furthermore, we study the GC-content of DNA codes and provide some examples of DNA codes with their respective deletion distance.