Locally recoverable codes from towers of function fields

2022/09/15 by María Chara, Chara, M., F. Galluccio +3 · 1 citation
Computer Science · #11G20 #11T71 #14H05 #94B27 #Advanced Data Storage Technologies #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2209.07136

openalex publication_date 2022/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbF_q² 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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• Quantum (r,δ)-Locally Recoverable BCH and Homothetic-BCH Codes

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