Optimal Cyclic Codes With Hierarchical Locality

Abstract

By introducing several levels of recoverability for locally recoverable codes (LRCs), LRCs with hierarchical locality (H-LRCs) are defined for correcting different numbers of erasures. There are two major ingredients in this paper. The first is to investigate some properties and existence conditions of optimal H-LRCs with respect to a generalized Singleton-like bound for H-LRCs. The second ingredient is to propose several constructions of optimal H-LRCs by employing cyclic codes. Notably, the parameters of these optimal H-LRCs are flexible.