Han Cai, Cuiling Fan, Ying Miao, Moshe Schwartz, Xiaohu Tang: Optimal Locally Repairable Codes: An Improved Bound and Constructions

Journal:IEEE Transactions on Information Theory

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 which 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.

Indexed by:SCI

Volume:68

Issue:8

Page Number:5060 - 5074

Translation or Not:no

Date of Publication:2022-08-15

Links to published journals:https://ieeexplore.ieee.org/document/9739761