English

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 Z4+ωZ4\Z_{4}+\omega \Z_{4}, where ω2=2+2ω\omega^{2}=2+2\omega along with methods to construct these with combinatorial constraints. We also generalize results obtained for the ring Z4+ωZ4\Z_{4}+\omega \Z_{4}, where ω2=2+2ω\omega^{2}=2+2\omega, and some other rings to the sixteen rings Rθ=Z4+ωZ4R_{\theta}=\Z_{4}+\omega \Z_{4}, where ω2=θZ4+ωZ4\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 RθR_{\theta} which enables us to attain an upper boundary for the Gau distance of free codes that are self-dual over the rings RθR_{\theta}.

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

R2 v1 2026-06-24T06:59:55.516Z