Two Classes of (r, t)-Locally Repairable Codes

Abstract. Locally repairable codes (LRCs) with (r,t)-locality allow each symbol to be repaired from at most r other symbols, and support up to t-1 simultaneous node repairs. We present two classes of (r,t)-LRCs with good parameters. The first class is constructed using combinatorial designs, achieving optimal minimum distance for certain parameter ranges. The second class is based on algebraic curves, providing flexibility in code rate and locality parameters. We analyze the trade-offs between locality, availability, and minimum distance for these constructions, and compare their parameters with existing bounds. Our constructions enrich the family of known (r,t)-LRCs and provide practical options for distributed storage systems requiring multiple repair alternatives.