On cooperative local repair in distributed storage

Erasure-correcting codes, that support local repair of codeword symbols, have attracted substantial attention recently for their application in distributed storage systems. In this paper we study a generalization of the usual locally recoverable codes. We consider such codes that any small set of codeword symbols is recoverable from a small number of other symbols. We call this cooperative local repair. We present bounds on the dimension of such codes as well as give explicit constructions of families of codes. Some other results regarding cooperative local repair are also presented, including an analysis for the Hadamard codes.