Uniform Minors in Maximally Recoverable Codes
Information Theory
2019-06-07 v1 math.IT
Abstract
In this letter, locally recoverable codes with maximal recoverability are studied with a focus on identifying the MDS codes resulting from puncturing and shortening. By using matroid theory and the relation between MDS codes and uniform minors, the list of all the possible uniform minors is derived. This list is used to improve the known non-asymptotic lower bound on the required field size of a maximally recoverable code.
Cite
@article{arxiv.1906.02423,
title = {Uniform Minors in Maximally Recoverable Codes},
author = {Matthias Grezet and Thomas Westerbäck and Ragnar Freij-Hollanti and Camilla Hollanti},
journal= {arXiv preprint arXiv:1906.02423},
year = {2019}
}