DNA cyclic codes over the ring<inf>2</inf>[ u, v ] / (u²- 1, v³- V, u v - V u)

Abstract

© 2018 World Scientific Publishing Company. In this paper, our main objective is to find out the necessary and sufficient conditions for a cyclic code of arbitrary length over the ring of four elements R1 = 2 + u2 (u2 = 1) to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring R = 2[u,v]/(u2 - 1,v3 - v,uv - vu), which plays an important role in Computational Biology. Furthermore, we establish a direct link between the elements of ring R and 64 codons used in the amino acids of living organisms by introducing a Gray map from R to R1. Among others, binary images of cyclic codes over R are also investigated. As applications, some cyclic DNA codes over R using the Gray map are provided.