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We study monomial-Cartesian codes (MCCs) which can be regarded as$(r,\delta)$-locally recoverable codes (LRCs). These codes come with a naturalbound 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 withthe 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.

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