  Distributed and cloud storage systems are used to reliably store large-scale
data. Erasure codes have been recently proposed and used in real-world
distributed and cloud storage systems such as Google File System, Microsoft
Azure Storage, and Facebook HDFS-RAID, to enhance the reliability. In order to
decrease the repair bandwidth and disk I/O, a class of erasure codes called
locally repairable codes (LRCs) have been proposed which have small locality
compare to other erasure codes. Although LRCs have small locality, they have
lower minimum distance compare to the Singleton bound. Hence, seeking the
largest possible minimum distance for LRCs have been the topic of many recent
studies. In this paper, we study the largest possible minimum distance of a
class of LRCs and evaluate them in terms of achievability. Furthermore, we
compare our results with the existence bounds in the literature.
