Compartmented Secret Sharing Schemes and Locally Repairable Codes

Multipartite secret sharing is an important research object in the area of secret sharing schemes. Compartmented access structures are an interesting class of multipartite access structures. The constructions of ideal linear schemes realizing compartmented access structures are studied by codes in this paper. We find that compartmented secret sharing is related to a class of codes called locally repairable codes which are being used widely in distributed and cloud storage systems. We study secret sharing schemes for compartmented access structures with upper bounds, compartmented access structures with lowers bounds and compartmented access structures with upper and lower bounds. We establish the relationships between secret sharing schemes for these compartmented access structures and locally repairable codes. Based on the relationships and some locally repairable codes, we obtain ideal linear schemes realizing these compartmented access structures by efficient methods.