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In this paper we construct new optimal hierarchical locally recoverablecodes. Our construction is based on a combination of the ideas of\cite{ballentine2019codes,sasidharan2015codes} with an algebraic numbertheoretical approach that allows to give a finer tuning of the minimum distanceof the intermediate code (allowing larger dimension of the final code), and toremove restrictions on the arithmetic properties of $q$ compared with the sizeof the locality sets in the hierarchy. In turn, we manage to obtain codes witha wide set of parameters both for the size $q$ of the base field, and for thehierarchy size, while keeping the optimality of the codes we construct.

Optimal locally recoverable codes with hierarchy from nested $F$-adic expansions