  Locally repairable codes (LRCs) have received significant recent attention as
a method of designing data storage systems robust to server failure. Optimal
LRCs offer the ideal trade-off between minimum distance and locality, a measure
of the cost of repairing a single codeword symbol. For optimal LRCs with
minimum distance greater than or equal to 5, block length is bounded by a
polynomial function of alphabet size. In this paper, we give explicit
constructions of optimal-length (in terms of alphabet size), optimal LRCs with
minimum distance equal to 5.
