Maximum Distance Separable Codes in the ρ Metric over Arbitrary Alphabets
Journal of Algebraic Combinatorics: An International Journal
The automorphism group of a linear space with the Rosenbloom—Tsfasman metric
European Journal of Combinatorics
Maximum Distance Codes in Matn,s (Zk) with a Non-Hamming Metric and Uniform Distributions
Designs, Codes and Cryptography
Fundamentals of wireless communication
Fundamentals of wireless communication
A class of Sudan-decodable codes
IEEE Transactions on Information Theory
Approximately universal codes over slow-fading channels
IEEE Transactions on Information Theory
On the Existence of Universally Decodable Matrices
IEEE Transactions on Information Theory
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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 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.