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Computing sharp recovery structures for locally recoverable codes

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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. In this article we develop an algorithm that computes a recovery structure as concise as possible for an arbitrary linear code \({\mathcal {C}}\) and a recovery method that realizes it. This algorithm also provides the locality and the dual distance of \({\mathcal {C}}\). Complexity issues are studied as well. Several examples are included.

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Authors and Affiliations

  1. Department of Mathematics, Statistics and O. Research, University of La Laguna, 38200, La Laguna, Tenerife, Spain

    Irene Márquez-Corbella

  2. Institute of Mathematics, University of Valladolid, Campus “Miguel Delibes”, 47011, Valladolid, Castilla, Spain

    Edgar Martínez-Moro

  3. Department of Applied Mathematics, University of Valladolid, Avda Salamanca SN, 47014, Valladolid, Castilla, Spain

    Carlos Munuera

Authors
  1. Irene Márquez-Corbella
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  2. Edgar Martínez-Moro
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  3. Carlos Munuera
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Correspondence to Irene Márquez-Corbella.

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Edgar Martinez-Moro and Carlos Munuera are supported by the Spanish State Research Agency (AEI) under Grant PGC2018-096446-B-C21.

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Codes, Cryptology and Curves”.

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Márquez-Corbella, I., Martínez-Moro, E. & Munuera, C. Computing sharp recovery structures for locally recoverable codes. Des. Codes Cryptogr. 88, 1687–1698 (2020). https://doi.org/10.1007/s10623-020-00746-7

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  • DOI: https://doi.org/10.1007/s10623-020-00746-7

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