  This work deals with partial MDS (PMDS) codes, a special class of locally
repairable codes, used for distributed storage system. We first show that a
known construction of these codes, using Gabidulin codes, can be extended to
use any maximum rank distance code. Then we define a standard form for the
generator matrices of PMDS codes and use this form to give an algebraic
description of PMDS generator matrices. This implies that over a sufficiently
large finite field a randomly chosen generator matrix in PMDS standard form
generates a PMDS code with high probability. This also provides sufficient
conditions on the field size for the existence of PMDS codes.
