Multi-point codes from the GGS curves
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May 2020, 14(2): 265-278. doi: 10.3934/amc.2020019
Locally recoverable codes from algebraic curves with separated variables
Carlos Munuera 1,, , Wanderson Tenório 2, and Fernando Torres 3,
Department of Applied Mathematics, University of Valladolid, Avda Salamanca SN, 47014, Valladolid, Castilla, Spain
Departamento de Matemática, Universidade Federal de Mato Grosso, Av. F. C. Costa 2367, 78060-900, Cuiabá, Brazil
Institute of Mathematics, Statistics and Computer Science, University of Campinas, Cidade Universitaria "Zeferino Vaz", Barão Geraldo, 13083-859, Campinas, Brazil
Received June 2018 Published May 2020 Early access September 2019
Fund Project: 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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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.
Keywords: Error-correcting code, locally recoverable code, algebraic geometry code.
Mathematics Subject Classification: 94B27, 11G20, 11T71, 14G50, 94B05.
Citation: Carlos Munuera, Wanderson Tenório, Fernando Torres. Locally recoverable codes from algebraic curves with separated variables. Advances in Mathematics of Communications, 2020, 14 (2) : 265-278. doi: 10.3934/amc.2020019
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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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Carlos Munuera Wanderson Tenório Fernando Torres