Hadamard Matrices, Baumert-Hall Units, Four-Symbol Sequences, Pulse Compression, and Surface Wave Encodings

Abstract If a Williamson matrix of order 4w exists and a special type of design, a set of Baumert-Hall units of order 4t, exists, then there exists a Hadamard matrix of order 4tw. A number of special Baumert-Hall sets of units, including an infinite class, are constructed here; these give the densest known classes of Hadamard matrices. The constructions relate to various topics such as pulse compression and image encodings.

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