Locally recoverable codes from towers of function fields

Abstract

In this work we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bound for the parameters of the obtained codes. In a particular case of a tower over ${\mathbb{F}}_{q^2}$ for any odd $q$, defined by Garcia and Stichtenoth in [GS2007], we show that the bound is sharp for the first code in the sequence, and we include a detailed analysis for the following codes in the sequence based on the distribution of rational places that split completely in the considered function field extension.