  Universally decodable matrices (UDMs) can be used for coding purposes when
transmitting over slow fading channels. These matrices are parameterized by
positive integers $L$ and $N$ and a prime power $q$. The main result of this
paper is that the simple condition $L \leq q+1$ is both necessary and
sufficient for $(L,N,q)$-UDMs to exist. The existence proof is constructive and
yields a coding scheme that is equivalent to a class of codes that was proposed
by Rosenbloom and Tsfasman. Our work resolves an open problem posed recently in
the literature.
