Optimal locally recoverable codes with hierarchy from nested $F$-adic expansions
Information Theory
2022-07-22 v1 math.IT
Number Theory
Abstract
In this paper we construct new optimal hierarchical locally recoverable codes. Our construction is based on a combination of the ideas of \cite{ballentine2019codes,sasidharan2015codes} with an algebraic number theoretical approach that allows to give a finer tuning of the minimum distance of the intermediate code (allowing larger dimension of the final code), and to remove restrictions on the arithmetic properties of compared with the size of the locality sets in the hierarchy. In turn, we manage to obtain codes with a wide set of parameters both for the size of the base field, and for the hierarchy size, while keeping the optimality of the codes we construct.
Cite
@article{arxiv.2207.10383,
title = {Optimal locally recoverable codes with hierarchy from nested $F$-adic expansions},
author = {Austin Dukes and Giacomo Micheli and Vincenzo Pallozzi Lavorante},
journal= {arXiv preprint arXiv:2207.10383},
year = {2022}
}
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