Locally recoverable codes from towers of function fields
Information Theory
2022-09-16 v1 math.IT
Number Theory
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 for any odd , 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.
Keywords
Cite
@article{arxiv.2209.07136,
title = {Locally recoverable codes from towers of function fields},
author = {M. Chara and F. Galluccio and E. Martínez-Moro},
journal= {arXiv preprint arXiv:2209.07136},
year = {2022}
}