Abstract
In this paper we construct new DNA cyclic codes over rings. Firstly, we introduce a new family of DNA cyclic codes over the ring $R=\mathbb{F}_2[u]/(u.6)$. A direct link between the elements of such a ring and the $64$ codons used in the amino acids of the living organisms is established. Using this correspondence we study the reverse-complement properties of our codes. We use the edit distance between the codewords which is an important combinatorial notion for the DNA strands. Next, we define the Lee weight, the Gray map over the ring $R$ as well as the binary image of the DNA cyclic codes allowing the transfer of studying DNA codes into studying binary codes. Secondly, we introduce another new family of DNA skew cyclic codes constructed over the ring $\tilde {R}=\mathbb{F}_2+v\mathbb{F}_2=\{0, 1, v, v+1\}, $ where $v^2=v$. The codes obtained are cyclic reverse-complement over the ring $\tilde {R}$. Further we find their binary images and construct some explicit examples of such codes.
Highlights
DNA computing combines genetic data analysis with the computational science in order to tackle computationally difficult problems
We shall give the structure of the cyclic reversible-complement DNA codes over the ring R with designed edit distance D
In the second part of the paper, we study the DNA skew cyclic codes over the ring R = F2 + vF2 = {0, 1, v, v + 1}, where v2 = v
Summary
DNA computing combines genetic data analysis with the computational science in order to tackle computationally difficult problems. We shall give the structure of the cyclic reversible-complement DNA codes over the ring R with designed edit distance D. The properties of our codes are the most required properties for DNA computing; namely, our codes are reversible-complement and cyclic which is a very important property, since it can reduce the complexity of the dynamic programming when testing the strand from the unwanted secondary structures [14]. The cyclic character of the DNA strands is desired because the genetic code should represent an equilibrium status [18] Another advantage of cyclic codes, as indicated by Milenkovic and Kashyap [14], is that the complexity of the dynamic programming algorithm for testing DNA codes for secondary structure will be less for cyclic codes. Many reversecomplement DNA code could be obtained in a skew polynomial ring (which is not the case in a commutative ring)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
