New DNA Codes from Cyclic Codes over Mixed Alphabets

Let R=F4+uF4,withu2=u and S=F4+uF4+vF4,withu2=u,v2=v,uv=vu=0. In this paper, we study F4RS-cyclic codes of block length (α,β,γ) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]〈xα−1〉×R[x]〈xβ−1〉×S[x]〈xγ−1〉. We discuss their generator polynomials as well as the structure of separable codes. Using the structure of separable codes, we study cyclic DNA codes. By using Gray maps ψ1 from R to F42 and ψ2 from S to F43, we give a one-to-one correspondence between DNA codons of the alphabets {A,T,G,C}2,{A,T,G,C}3 and the elements of R,S, respectively. Then we discuss necessary and sufficient conditions of cyclic codes over F4, R, S and F4RS to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results.