Asymptotic Bounds on the Rate of Locally Repairable Codes

DOI10.1109/TIT.2021.3131003zbMATH Open1495.94164arXiv2010.14492OpenAlexW3216044229MaRDI QIDQ5080013

Ron M. Roth

Publication date: 30 May 2022

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: New asymptotic upper bounds are presented on the rate of sequences of locally repairable codes (LRCs) with a prescribed relative minimum distance and locality over a finite field $F$. The bounds apply to LRCs in which the recovery functions are linear; in particular, the bounds apply to linear LRCs over $F$. The new bounds are shown to improve on previously published results, especially when the repair groups are disjoint, namely, they form a partition of the set of coordinates.

Full work available at URL: https://arxiv.org/abs/2010.14492

zbMATH Keywords

locally repairable codesasymptotic upper bounds

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Bounds on codes (94B65)

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