A survey on optimal locally repairable codes

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