An Upper Bound On the Size of Locally Recoverable Codes
In a locally recoverable or repairable code, any symbol of a codeword can be recovered by reading only a small (constant) number of other symbols. The notion of local recoverability is important in the area of distributed storage where a most frequent error-event is a single storage node failure (erasure). A common objective is to repair the node by downloading data from as few other storage nodes as possible. In this paper, the authors bound the minimum distance of a code in terms of its length, size and locality. Unlike previous bounds, their bound follows from a significantly simple analysis and depends on the size of the alphabet being used.