Locally recoverable codes from towers of function fields

GALLUCCIO FRANCISCO

Marsella

Congreso; Conference On alGebraic varieties over fiNite fields and Algebraic geometry Codes; 2023

Centre International de Rencontres Mathématiques

In this work, we construct sequences of locally recoverable AG codes arising from a tower of function fields and give bounds for the parameters of the obtained codes. In a particular case of a tower over Fq2 for any odd q, defined by Garcia and Stichtenoth, we show that the bound is sharp for the first code in the sequence. 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.