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\iteman{io-port 05193327}
\itemau{Vontobel, Pascal O.; Ganesan, Ashwin}
\itemti{On universally decodable matrices for space-time coding.}
\itemso{Des. Codes Cryptography 41, No. 3, 325-342 (2006).}
\itemab
Summary: The notion of universally decodable matrices (UDMs) was recently introduced by {\it S. Tavildar} and {\it P. Viswanath} [IEEE Trans. Inf. Theory 52, No. 7, 3233--3258 (2006)] 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 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 {\it M. Yu. Rosenbloom} and {\it M. A. Tsfasman} [Probl. Inf. Transm. 33, No. 1, 45--52 (1997; Zbl 1037.94545)]. Moreover, we point out connections to so-called repeated-root cyclic codes.
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\itemut{Universally decodable matrices; Coding for slow-fading channels; Rank condition; Efficient decoding; Rosenbloom-Tsfasman metric; Reed-Solomon codes; Repeated-root cyclic codes; Hasse derivatives; Newton interpolation; Pascal's triangle}
\itemli{doi:10.1007/s10623-006-9019-4}
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