Explicit and optimal codes for distributed storage
In the distributed storage coding problem we consider, data is stored across n nodes in a network, each capable of storing α symbols. It is required that the complete data can be reconstructed by downloading data from any k nodes. There is also the key additional requirement that a failed node be regenerated by connecting to any d nodes and downloading β symbols from each of them. Our goal is to minimize the repair bandwidth dβ. In this paper we provide explicit constructions for several parameter sets of interest.