Asymptotic Bounds on the Rate of Locally Repairable Codes

10/27/2020

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by   Ron M. Roth, et al.

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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.