Repair Locality with Multiple Erasure Tolerance

Abstract. Locally repairable codes (LRCs) are erasure codes designed for distributed storage systems that enable efficient repair of a single failed storage node by accessing only a small number of other nodes. This paper extends the study of LRCs to the scenario of multiple erasures. We derive fundamental bounds on the parameters of codes that can tolerate multiple erasures while maintaining the locality property. Specifically, we establish an upper bound on the code dimension given the code length, minimum distance, and locality parameters for the multiple-erasure case. We also present explicit code constructions that achieve the derived bounds, demonstrating the optimality of our results. The constructions are based on algebraic and combinatorial methods and provide practical LRCs for storage systems that need to handle multiple simultaneous node failures.