Do non-free LCD codes over finite commutative Frobenius rings exist?
Abstract
In this paper, we clarify some aspects on LCD codes in the literature. We first prove that a non-free LCD code does not exist over finite commutative Frobenius local rings. We then obtain a necessary and sufficient condition for the existence of LCD code over finite commutative Frobenius rings. We later show that a free constacyclic code over finite chain ring is LCD if and only if it is reversible, and also provide a necessary and sufficient condition for a constacyclic code to be reversible over finite chain rings. We illustrate the minimum Lee-distance of LCD codes over some finite commutative chain rings and demonstrate the results with examples. We also got some new optimal codes of different lengths {which are} cyclic LCD codes over .
Keywords
Cite
@article{arxiv.1901.10836,
title = {Do non-free LCD codes over finite commutative Frobenius rings exist?},
author = {Sanjit Bhowmick and Alexandre Fotue-Tabue and Edgar Martínez-Moro and Ramakrishna Bandi and Satya Bagchi},
journal= {arXiv preprint arXiv:1901.10836},
year = {2019}
}