Constructions of Optimal Cyclic Codes With h-Level Hierarchical Locality

In order to correct different numbers of erasures in distributed storage systems, the design of locally repairable codes with hierarchical locality (H-LRCs) is crucial. In this paper, we study h -level H-LRCs where h is not limited to 2. We present four constructions of cyclic h -level H-LRCs with length ln such that gcd( l , q ) = 1 and n |( q −1). These four classes of cyclic h -level H-LRCs are optimal with respect to the generalized Singleton-like bound. The minimum Hamming distances of them are d = δ, δ+1, δ+2, δ+δ respectively. Furthermore, these four classes of cyclic h -level H-LRCs have new and flexible parameters which are not covered in the literature. By setting the parameter l appropriately for the third construction, one can construct optimal cyclic h -level H-LRCs with length n |( q −1) and distance d = δ+σ where σ is not limited to 0, 1, 2, δ .