Locally recoverable codes from algebraic curves with separated variables

Carlos Munuera; Wanderson Tenório; Fernando Torres

doi:10.3934/amc.2020019

Article Contents

2020, Volume 14, Issue 2: 265-278. Doi: 10.3934/amc.2020019

This issue Previous Article Constructing 1-resilient rotation symmetric functions over

$ {\mathbb F}_{p} $

with

$ {q} $

variables through special orthogonal arrays Next Article Multi-point codes from the GGS curves

Locally recoverable codes from algebraic curves with separated variables

1.
Department of Applied Mathematics, University of Valladolid, Avda Salamanca SN, 47014, Valladolid, Castilla, Spain
2.
Departamento de Matemática, Universidade Federal de Mato Grosso, Av. F. C. Costa 2367, 78060-900, Cuiabá, Brazil
3.
Institute of Mathematics, Statistics and Computer Science, University of Campinas, Cidade Universitaria "Zeferino Vaz", Barão Geraldo, 13083-859, Campinas, Brazil

^* Corresponding author
^* Corresponding author

Received: May 31, 2018

Early access: September 2019

Published: May 2020

The first author was supported by Spanish Ministerio de Economía y Competitividad under grant MTM2015-65764-C3-1-P MINECO/FEDER. The second author was supported by CNPq-Brazil, under grants 201584/2015-8 and 159852/2014-5. The third author was supported by CNPq-Brazil under grant 310623/2017-0

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Abstract

A Locally Recoverable code is an error-correcting code such that any erasure in a single coordinate of a codeword can be recovered from a small subset of other coordinates. We study Locally Recoverable Algebraic Geometry codes arising from certain curves defined by equations with separated variables. The recovery of erasures is obtained by means of Lagrangian interpolation in general, and simply by one addition in some particular cases.

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Mathematics Subject Classification: 94B27, 11G20, 11T71, 14G50, 94B05.

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Table 1. Hamming weights of Example 5

$ t $	1	2	3	4	5	6
lower bound (9)	10	12	13	14	15	16
upper bound (8)	11	12	14	15	17	18

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References

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