Asymptotic Bounds on the Rate of Locally Repairable Codes

Ron M. Roth

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arXiv · 2010.14492

Asymptotic Bounds on the Rate of Locally Repairable Codes

Ron M. Roth

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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.

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Ron M. Roth. 2020-10-27. Asymptotic Bounds on the Rate of Locally Repairable Codes. https://arxiv.org/abs/2010.14492

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