DNA cyclic codes over the ring ð ½2[u,v]/〈u2 − 1,v3 − v,uv − vu〉 - Hai Q. Dinh (2018)
© 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 (Formula presented.) (Formula presented.) to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring (Formula presented.), which plays an important role in Computational Biology. Furthermore, we establish a direct link between the elements of ring (Formula presented.) and 64 codons used in the amino acids of living organisms by introducing a Gray map from (Formula presented.) to (Formula presented.). Among others, binary images of cyclic codes over (Formula presented.) are also investigated. As applications, some cyclic DNA codes over (Formula presented.) using the Gray map are provided.