On minimum distance of locally repairable codes

Distributed and cloud storage systems are used to reliably store large-scale data. To enhance data reliability, erasure codes have been recently proposed and used in real-world distributed and cloud storage systems. Conventional erasure codes are not suitable for distributed storage systems, as they cause significant repair bandwidth and disk I/O. As a solution, a class of erasure codes called locally repairable codes (LRCs) have been proposed, where repairing failed nodes requires access to a small number of available nodes, hence reducing the repair bandwidth and disk I/O. Because of their practical importance, LRCs and in particular their achievable minimum distance have been the topic of many recent studies. In this paper, we find an achievable bound on the minimum distance of a class of LRCs. Furthermore, we show how to construct codes that achieve our proposed bound and compare our results with the existing bounds in the literature.