New DNA codes from cyclic codes over mixed alphabets

Abstract

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Let R = F4 + uF4, with u2 = u and S = F4 + uF4 + vF4, with u2 = u, v2 = v, uv = vu = 0. In this paper, we study F4 RS-cyclic codes of block length (α, β, γ) and construct cyclic DNA codes from them. F4 RS-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 F24 and ψ2 from S to F34, 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 F4 RS to be reversible and reverse-complement. As applications, we provide examples of new cyclic DNA codes constructed by our results.