Repair Locality from a Combinatorial Perspective

Abstract. We study repair locality in distributed storage from a combinatorial perspective. Locally repairable codes (LRCs) allow the repair of a failed node by accessing only a small number of other nodes, called the repair locality. We derive new bounds on the parameters of LRCs using combinatorial arguments, providing tight constraints on the relationship between code length, dimension, minimum distance, and locality. Our combinatorial approach reveals structural properties of LRCs that are not captured by algebraic methods. We also present code constructions based on combinatorial designs that achieve the derived bounds, demonstrating their tightness. This work provides a systematic combinatorial framework for understanding the fundamental limits of LRCs.