New DNA Codes from Cyclic Codes over Mixed Alphabets

Let R = F-4 + uF(4), with u(2) = u and S = F-4 + uF(4) + vF(4),with u(2) = u, v(2)= v, uv = vu = 0. In this paper, we study F4RS-cyclic codes of block length (alpha,beta,gamma) and construct cyclic DNA codes from them. F4RS-cyclic codes can be viewed as S[x]-submodules of Fq[x]/< x(alpha)-1 > x R[x]/< x(beta)-1 &> x S[x]< x(gamma)-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 psi(1) from R to F-4(2) and psi(2) from S to F(4)3, 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 F-4, R, S and F4RS to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results.