DNA Cyclic Codes Over The Ring $ \F_2[u,v]/\langle u^2-1,v^3-v,uv-vu \rangle$
Information Theory
2015-11-13 v1 math.IT
Abstract
In this paper, we mainly study the some structure of cyclic DNA codes of odd length over the ring which play an important role in DNA computing. We established a direct link between the element of ring and 64 codons by introducing a Gray map from to where is the ring of four elements. The reverse constrain and the reverse-complement constraint codes over and are studied in this paper. Binary image of the cyclic codes over R also study. The paper concludes with some example on DNA codes obtained via gray map.
Keywords
Cite
@article{arxiv.1511.03937,
title = {DNA Cyclic Codes Over The Ring $ \F_2[u,v]/\langle u^2-1,v^3-v,uv-vu \rangle$},
author = {Sukhamoy Pattanayak and Abhay Kumar Singh and Pratyush Kumar},
journal= {arXiv preprint arXiv:1511.03937},
year = {2015}
}
Comments
17 pages, 4 Tables(Table 1 contained 2 pages). arXiv admin note: substantial text overlap with arXiv:1508.02015; text overlap with arXiv:1508.07113, arXiv:1505.06263 by other authors