Optimal Linear and Cyclic Locally Repairable Codes over Small Fields

Abstract : We consider locally repairable codes over small fields and propose constructions of optimal cyclic and linear codes in terms of the dimension for a given distance and length. Four new constructions of optimal linear codes over small fields with locality properties are developed. The first two approaches give binary cyclic codes with locality two. While the first construction has availability one, the second binary code is characterized by multiple available repair sets based on a binary Simplex code. The third approach extends the first one to q-ary cyclic codes including (binary) extension fields, where the locality property is determined by the properties of a shortened first-order Reed-Muller code. Non-cyclic optimal binary linear codes with locality greater than two are obtained by the fourth construction.
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Communication dans un congrès
IEEE Information Theory Workshop (ITW) 2015, Apr 2015, Jerusalem, Israel
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https://hal.inria.fr/hal-01117826
Contributeur : Alexander Zeh <>
Soumis le : mercredi 18 février 2015 - 08:35:01
Dernière modification le : dimanche 31 décembre 2017 - 09:44:02
Document(s) archivé(s) le : mardi 19 mai 2015 - 10:11:38

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CyclicLRCcameraready.pdf
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  • HAL Id : hal-01117826, version 1
  • ARXIV : 1502.06809

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Alexander Zeh, Eitan Yaakobi. Optimal Linear and Cyclic Locally Repairable Codes over Small Fields. IEEE Information Theory Workshop (ITW) 2015, Apr 2015, Jerusalem, Israel. 〈hal-01117826〉

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