Optimal (r,δ)-LRCs from monomial-Cartesian codes and their subfield-subcodes · arXivDesk
2205.01485May 3, 2022This is a revised version of the manuscript "Optimal $(r,δ)$-LRCs from zero-dimensional affine variety codes and their subfield-subcodes". We have modified the title and the new one is "Optimal $(r,δ)$-LRCs from monomial-Cartesian codes and their subfield-subcodes". This new version contains rather changes, the main ones appear in Section 4
Optimal (r,δ)-LRCs from monomial-Cartesian codes and their subfield-subcodes
Carlos Galindo, Fernando Hernando, Helena Martín-Cruz
We study monomial-Cartesian codes (MCCs) which can be regarded as (r,δ)-locally recoverable codes (LRCs). These codes come with a natural bound for their minimum distance and we determine those giving rise to (r,δ)-optimal LRCs for that distance, which are in fact (r,δ)-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,δ)