Cyclic DNA codes over the ring F<inf>2</inf>+ uF<inf>2</inf>+ vF<inf>2</inf>+ uvF<inf>2</inf>+ v²F<inf>2</inf>+ uv²F<inf>2</inf>

• Main Authors: Hai Q. Dinh, Abhay Kumar Singh, Sukhamoy Pattanayak, Songsak Sriboonchitta
• Format: Journal
• Published: 2018
• Subjects: Computer Science; Mathematics
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85027868324&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/58489
• Institution: Chiang Mai University

© 2017, Springer Science+Business Media, LLC. 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.