On the Existence of Universally Decodable Matrices
<|reference_start|>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 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.<|reference_end|>
@article{ganesan2006on,
    title={On the Existence of Universally Decodable Matrices},
    author={Ashwin Ganesan, Pascal O. Vontobel},
    journal={arXiv preprint arXiv:cs/0601066},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0601066},
    primaryClass={cs.IT cs.DM math.IT}
}