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An Explicit Construction of Universally Decodable Matrices
Universally decodable matrices can be used for coding purposes when
transmitting over slow fading channels. These matrices are parameterized by
positive integers and and a prime power . Based on Pascal's triangle
we give an explicit construction of universally decodable matrices for any
non-zero integers and and any prime power where . This
is the largest set of possible parameter values since for any list of
universally decodable matrices the value is upper bounded by , except
for the trivial case . 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