Erasure codes with symbol locality and group decodability for distributed storage

We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {α, β, k, t}, where k is the number of information symbols, each codeword of an (α, β, k, t)- group decodable code is a t-tuple of strings, called buckets, such that each bucket is a string of β symbols that is a codeword of a [β, α] MDS code (which is encoded from α information symbols). Such codes have the following two properties: (P1) Locally Repairable: Each code symbol has locality (α, β - α + 1). (P2) Group decodable: From each bucket we can decode α information symbols. We establish an upper bound of the minimum distance of (α, β, k, t)-group decodable code for any given set of {α, β, k, t}; We also prove that the bound is achievable when the coding field F has size |F| > (^n-1_k-1 ).