Cyclic and Quasi-Cyclic DNA Codes
Information Theory
2021-10-20 v1 math.IT
Rings and Algebras
Abstract
In this paper, we discuss DNA codes that are cyclic or quasi-cyclic over , where along with methods to construct these with combinatorial constraints. We also generalize results obtained for the ring , where , and some other rings to the sixteen rings , where , using the generalized Gau map and Gau distance in \cite{3}. We determine a relationship between the Gau distance and Hamming distance for linear codes over the sixteen rings which enables us to attain an upper boundary for the Gau distance of free codes that are self-dual over the rings .
Keywords
Cite
@article{arxiv.2110.09789,
title = {Cyclic and Quasi-Cyclic DNA Codes},
author = {Adel Alahmadi and Alaa Altassan and Amani Alyoubi and Manish K. Gupta and Hatoon Shoaib},
journal= {arXiv preprint arXiv:2110.09789},
year = {2021}
}
Comments
draft, 16 pages