  In this paper, locally repairable codes with all-symbol locality are studied.
Methods to modify already existing codes are presented. Also, it is shown that
with high probability, a random matrix with a few extra columns guaranteeing
the locality property, is a generator matrix for a locally repairable code with
a good minimum distance. The proof of this also gives a constructive method to
find locally repairable codes. Constructions are given of three infinite
classes of optimal vector-linear locally repairable codes over an alphabet of
small size, not depending on the size of the code.
