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arXiv · 1410.6339

Constructions and Properties of Linear Locally Repairable Codes

Toni Ernvall·Thomas Westerbäck·Camilla Hollanti·Ragnar Freij
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Abstract

In this paper, locally repairable codes with all-symbol locality are studied. Methods to modify already existing codes are presented. Also, it is shown that with high probability, a random matrix with a few extra columns guaranteeing the locality property, is a generator matrix for a locally repairable code with a good minimum distance. The proof of this also gives a constructive method to find locally repairable codes. Constructions are given of three infinite classes of optimal vector-linear locally repairable codes over an alphabet of small size, not depending on the size of the code.

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Toni Ernvall, Thomas Westerbäck, Camilla Hollanti, Ragnar Freij. 2014-10-23. Constructions and Properties of Linear Locally Repairable Codes. https://doi.org/10.1109/tit.2015.2512864

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