On reversible DNA codes over the ring Z₄[u,v]/ u²-2,uv-2,v²,2u,2v based on the deletion distance

Let R= Z₄[u,v]/ u²-2,uv-2,v²,2u,2v R=Z4[u,v]/⟨u2-2,uv-2,v2,2u,2v⟩ be a ring, where Z₄ Z4 is a ring of integers modulo 4. This ring R R is a local non-chain ring of characteristic 4. The main objective of this article is to construct reversible cyclic codes of odd length n over the ring R. R. Employing these reversible cyclic codes, we obtain reversible cyclic DNA codes of length n , based on the deletion distance over the ring R. R. We also construct a bijection Γ Γ between the elements of the ring R R and S_D₁₆. SD16. As an application of Γ , Γ, the reversibility problem which occurs in DNA k -bases has been solved. Moreover, we introduce a Gray map Ψ :Rⁿ→ F₂⁸ⁿ Ψhom:Rn→F28n with respect to homogeneous weight w whom over the ring R R . Further, we discuss the GC -content of DNA cyclic codes and their deletion distance. Moreover, we provide some examples of reversible DNA cyclic codes.