Bounds on the rate of linear locally repairable codes over small alphabets
Abhishek Agarwal, Arya Mazumdar · 2016
Locally repairable codes (LRC) have recently been a subject of intense research due to the theoretical appeal and their application in distributed storage systems. In an LRC, any coordinate of a codeword can be recovered by accessing only few other coordinates. For LRCs over small alphabet (such as binary), the optimal rate-distance trade-off is unknown. In this paper we provide the tightest known upper bound on the rate of linear LRCs of a given relative distance, an improvement over the best known bound by Cadambe and Mazumdar.