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DNA cyclic codes over the ring F2[u,v]/⟨u2−1,v3−v,uv−vu⟩

Authors: 

Hai Q. Dinh, Abhay Kumar Singh, Sukhamoy Pattanayak and Songsak Sriboonchitta

Source title: 
International Journal of Biomathematics, 11(3), 1850042 (19 pages), 2018 (ISI)
Academic year of acceptance: 
2018-2019
Abstract: 

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 R= F+ uF(u= 1) to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring = F2[u,v]/⟨u− 1, vv, 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.