MDS and MHDR cyclic codes over finite chain rings
Information Theory
2023-03-29 v1 math.IT
Abstract
In this work, a unique set of generators for a cyclic code over a finite chain ring has been established. The minimal spanning set and rank of the code have also been determined. Further, sufficient as well as necessary conditions for a cyclic code to be an MDS code and for a cyclic code to be an MHDR code have been obtained. Some examples of optimal cyclic codes have also been presented.
Cite
@article{arxiv.2303.15819,
title = {MDS and MHDR cyclic codes over finite chain rings},
author = {Monika Dalal and Sucheta Dutt and Ranjeet Sehmi},
journal= {arXiv preprint arXiv:2303.15819},
year = {2023}
}