Achieving Arbitrary Locality and Availability in Binary Codes

Abstract. We study the construction of binary locally repairable codes with arbitrary locality and availability parameters. Locality refers to the number of symbols needed to repair a failed node, while availability indicates the number of disjoint repair groups available for each symbol. We propose a general construction framework based on combinatorial designs that can achieve any desired locality r and availability t simultaneously. The constructed codes are binary, making them particularly suitable for practical storage systems. We analyze the parameters of the resulting codes, including their length, dimension, and minimum distance, and show that they achieve optimal or near-optimal trade-offs for many parameter regimes. Our construction provides the first systematic method for building binary LRCs with flexible locality and availability.