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 six classes of cyclic h-level H-LRCs which are optimal with respect to the generalized Singleton-like bound. The first five classes of cyclic h-level H-LRCs have length ln1 such that gcd(l, q) = 1, and n(1)|(q-1) or n(1)|(q + 1). The last class of cyclic h-level H-LRCs has length n|(q+1). The minimum Hamming distances of them are d = delta(1)+i where i can take 0, 2, delta(h), and so on. Furthermore, these six classes of cyclic h-level H-LRCs have new parameters which are not covered in the literature.