DNA Codes over the Ring $\mathbb{Z}_4 + w\mathbb{Z}_4$
Adel Alahmadi, Krishna Gopal Benerjee, Sourav Deb, Manish K, Gupta

TL;DR
This paper generalizes the construction and analysis of DNA codes over rings 4 + w4, introducing new bounds, code classes, and mappings, and explores their properties including duality and reverse constraints.
Contribution
It extends the Gau map and distance to all rings 4 + w4, establishes isometries, and constructs optimal DNA codes satisfying reverse and reverse-complement constraints.
Findings
Established bounds like Sphere Packing, GV, Singleton, and Plotkin over the rings.
Constructed optimal codes with respect to these bounds.
Proposed DNA code families satisfying reverse and reverse-complement constraints.
Abstract
In this present work, we generalize the study of construction of DNA codes over the rings , for . Rigorous study along with characterization of the ring structures is presented. We extend the Gau map and Gau distance, defined in \cite{DKBG}, over all the rings . Furthermore, an isometry between the codes over the rings and the analogous DNA codes is established in general. Brief study of dual and self dual codes over the rings is given including the construction of special class of self dual codes that satisfy reverse and reverse-complement constraints. The technical contributions of this paper are twofold. Considering the Generalized Gau distance, Sphere Packing-like bound, GV-like bound, Singleton like bound and Plotkin-like bound are…
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Taxonomy
TopicsDNA and Biological Computing · Advanced biosensing and bioanalysis techniques · Coding theory and cryptography
