Codes on Curves with Hierarchical Locality

Locally recoverable (LRC) codes provide ways of recovering erased coordinates of the codeword without having to access each of the remaining coordinates. A subfamily of LRC codes with hierarchical locality (H-LRC codes) provides added flexibility to the construction by introducing several tiers of recoverability for correcting different numbers of erasures. We present a general construction of codes on algebraic curves that have 2-level hierarchical locality and give a number of examples of such code families.