Optimal $(r,\delta)$-LRCs from monomial-Cartesian codes and their subfield-subcodes
Abstract
We study monomial-Cartesian codes (MCCs) which can be regarded as -locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to -optimal LRCs for that distance, which are in fact -optimal. A large subfamily of MCCs admits subfield-subcodes with the same parameters of certain optimal MCCs but over smaller supporting fields. This fact allows us to determine infinitely many sets of new -optimal LRCs and their parameters.
Cite
@article{arxiv.2205.01485,
title = {Optimal $(r,\delta)$-LRCs from monomial-Cartesian codes and their subfield-subcodes},
author = {Carlos Galindo and Fernando Hernando and Helena Martín-Cruz},
journal= {arXiv preprint arXiv:2205.01485},
year = {2024}
}
Comments
This is a revised version of the manuscript "Optimal $(r,\delta)$-LRCs from zero-dimensional affine variety codes and their subfield-subcodes". We have modified the title and the new one is "Optimal $(r,\delta)$-LRCs from monomial-Cartesian codes and their subfield-subcodes". This new version contains rather changes, the main ones appear in Section 4