Optimal $(r,\delta)$-LRCs from monomial-Cartesian codes and their subfield-subcodes

Carlos Galindo; Fernando Hernando; Helena Martín-Cruz

doi:10.1007/s10623-024-01403-z

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arXiv · 2205.01485

Optimal $(r,\delta)$-LRCs from monomial-Cartesian codes and their subfield-subcodes

Carlos Galindo·Fernando Hernando·Helena Martín-Cruz

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Abstract

We study monomial-Cartesian codes (MCCs) which can be regarded as $(r,\delta)$-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to $(r,\delta)$-optimal LRCs for that distance, which are in fact $(r,\delta)$-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 $(r,\delta)$-optimal LRCs and their parameters.

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Carlos Galindo, Fernando Hernando, Helena Martín-Cruz. 2022-05-03. Optimal $(r,\delta)$-LRCs from monomial-Cartesian codes and their subfield-subcodes. https://doi.org/10.1007/s10623-024-01403-z

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