Reversible cyclic codes over F4 + uF4 and their applications to DNA codes

In this paper we study the structure of reversible cyclic codes of both even and odd lengths over the ring R = F₄ + uF₄, u² = 0. We present necessary and sufficient conditions for a cyclic code over R to be reversible-complement. We also study cyclic DNA codes over nucleotide base pairs S(D₁₆), where S(D₁₆) = {GG, GA, GC, GT, CC, CA, CG, CT, AA, AT, AG, AC, TT, TA, TG, TC}. For this we first establish a one-to-one correspondence between R and S(D₁₆), and then cyclic DNA codes are constructed over S(D₁₆) as the images of reversible-complement cyclic codes over R.