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Cyclic DNA codes over the ring F2 + uF2 + vF2 + uvF2 + v2F2 + uv2F2

Authors: 

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

Source title: 
Designs, Codes and Cryptography, 86(7): 1451-1467, 2018 (ISI)
Academic year of acceptance: 
2017-2018
Abstract: 

We study the structure of cyclic DNA codes of odd length over the finite commutative ring R=F2+uF2+vF2+uvF2+v2F2+uv2F2, u2=0, v3=v, which plays an important role in genetics, bioengineering and DNA computing. A direct link between the elements of the ring R and 64 codons used in the amino acids of living organisms is established by introducing a Gray map from R to R1=F2+uF2 (u2=0). The reversible and the reversible-complement codes over R are investigated. We also discuss the binary image of the cyclic DNA codes over R. Among others, some examples of DNA codes obtained via Gray map are provided.