  Universally decodable matrices 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 $q$. Based on Pascal's triangle
we give an explicit construction of universally decodable matrices for any
non-zero integers $L$ and $n$ and any prime power $q$ where $L \leq q+1$. This
is the largest set of possible parameter values since for any list of
universally decodable matrices the value $L$ is upper bounded by $q+1$, except
for the trivial case $n = 1$. For the proof of our construction we use
properties of Hasse derivatives, and it turns out that our construction has
connections to Reed-Solomon codes, Reed-Muller codes, and so-called
repeated-root cyclic codes. Additionally, we show how universally decodable
matrices can be modified so that they remain universally decodable matrices.
