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

Abstract

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 Sd16, where Sd16 = {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 Sd16, and then cyclic DNA codes are constructed over Sd16 as the images of reversible-complement cyclic codes over R.