On the existence of universally decodable matrices
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 correspondence is that the simple condition L <= 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.
universally decodable matrices (udm) coding for slow fading channels full-rank condition rosenbloom-tsfasman codes