A survey on optimal locally repairable codes

Abstract

Locally repairable codes, or locally recoverable codes (LRC for short) are designed for application in distributed and cloud storage systems. Similar to the classical block codes, there is an important bound called the Singleton-type bound for locally repairable codes. In this paper, an optimal locally repairable code refers to a block code achieving this Singleton-type bound. Like the classical MDS (maximum distance separable) codes, the optimal locally repairable codes have some very nice combinatorial structures. Since the introduction of Singleton-type bound for locally repairable codes, people have put tremendous effort on constructions of optimal locally repairable codes. In this paper, we give a survey on optimal locally repairable codes,including bounds and constructions.