Asymptotic Bounds on the Rate of Locally Repairable Codes
Information Theory
2020-10-28 v1 math.IT
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 . The bounds apply to LRCs in which the recovery functions are linear; in particular, the bounds apply to linear LRCs over . 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.
Cite
@article{arxiv.2010.14492,
title = {Asymptotic Bounds on the Rate of Locally Repairable Codes},
author = {Ron M. Roth},
journal= {arXiv preprint arXiv:2010.14492},
year = {2020}
}