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arXiv · 2209.07136

Locally recoverable codes from towers of function fields

M. Chara·F. Galluccio·E. Martínez-Moro
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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.

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M. Chara, F. Galluccio, E. Martínez-Moro. 2022-09-15. Locally recoverable codes from towers of function fields. https://arxiv.org/abs/2209.07136

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