Optimal Locally Repairable Codes: An Improved Bound and Constructions
Information Theory
2020-11-11 v1 math.IT
Abstract
We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes that show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.
Cite
@article{arxiv.2011.04966,
title = {Optimal Locally Repairable Codes: An Improved Bound and Constructions},
author = {Han Cai and Cuiling Fan and Ying Miao and Moshe Schwartz and Xiaohu Tang},
journal= {arXiv preprint arXiv:2011.04966},
year = {2020}
}