  The notion of universally decodable matrices (UDMs) was recently introduced
by Tavildar and Viswanath while studying slow fading channels. It turns out
that the problem of constructing UDMs is tightly connected to the problem of
constructing maximum distance separable (MDS) codes. In this paper, we first
study the properties of UDMs in general and then we discuss an explicit
construction of a class of UDMs, a construction which can be seen as an
extension of Reed-Solomon codes. In fact, we show that this extension is, in a
sense to be made more precise later on, unique. Moreover, the structure of this
class of UDMs allows us to answer some open conjectures by Tavildar, Viswanath,
and Doshi in the positive, and it also allows us to formulate an efficient
decoding algorithm for this class of UDMs. It turns out that our construction
yields a coding scheme that is essentially equivalent to a class of codes that
was proposed by Rosenbloom and Tsfasman. Moreover, we point out connections to
so-called repeated-root cyclic codes.
