Constructions of Optimal Codes With Hierarchical Locality

Abstract

Locally repairable codes (LRCs) and codes with hierarchical locality (H-LRCs) have a great significance due to their applications in distributed storage systems. Constructing LRCs or H-LRCs achieving the Singleton-type bound is a challenging task and has received much attention. In this paper, we make use of optimal LRCs to construct a family of optimal H-LRCs. For this purpose we first construct a new class of optimal LRCs via generalized Reed-Solomon codes (GRS codes). Next, based on these optimal LRCs we present some new optimal H-LRCs, of which the parameters are more flexible than those given in [1] and [18].