Cyclic and QuasiCyclic DNA Codes
Abstract
In this paper, we discuss DNA codes that are cyclic or quasicyclic over $\Z_{4}+\omega \Z_{4}$, where $\omega^{2}=2+2\omega$ along with methods to construct these with combinatorial constraints. We also generalize results obtained for the ring $\Z_{4}+\omega \Z_{4}$, where $\omega^{2}=2+2\omega$, and some other rings to the sixteen rings $R_{\theta}=\Z_{4}+\omega \Z_{4}$, where $\omega^{2}=\theta\in \Z_{4}+\omega \Z_{4}$, 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 $R_{\theta}$ which enables us to attain an upper boundary for the Gau distance of free codes that are selfdual over the rings $R_{\theta}$.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09789
 Bibcode:
 2021arXiv211009789A
 Keywords:

 Computer Science  Information Theory;
 Mathematics  Rings and Algebras
 EPrint:
 draft, 16 pages