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Article Contents

# Locally recoverable codes from algebraic curves with separated variables

• * Corresponding author

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

• 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.

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

 Citation:

• 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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