Rank-metric codes with local recoverability

We construct rank-metric codes with locality constraints under the rank-metric. Our motivation stems from designing codes for efficient data recovery from correlated and/or mixed (i.e., complete and partial) failures in distributed storage systems. Specifically, the proposed local rank-metric codes can recover locally from crisscross failures, which affect a limited number of rows and/or columns of the storage system. First, we prove a Singleton-like upper bound on the minimum rank-distance of linear codes with rank-locality constraints. Second, we construct a family of locally recoverable rank-metric codes that achieve this bound for a broad range of parameters. The proposed construction builds upon Tamo and Barg's method for constructing locally repairable codes with optimal minimum Hamming distance.