Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings
TLDR
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.About:
This article is published in Journal of Combinatorial Theory, Series A.The article was published on 1974-05-01 and is currently open access. It has received 191 citations till now. The article focuses on the topics: Complex Hadamard matrix & Hadamard matrix.read more
Citations
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Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes
James A. Davis,Jonathan Jedwab +1 more
TL;DR: A previously unrecognized connection between Golay complementary sequences and second-order Reed-Muller codes over alphabets Z/sub 2/h is found to give an efficient decoding algorithm involving multiple fast Hadamard transforms.
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Polyphase complementary codes
TL;DR: A number of new results are presented including additional kernels and lengths of polyphase complementary codes, including complementary Barker codes, and a table of known lengths of pairs, triads and quads of sequences is given.
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A Hadamard matrix of order 428
TL;DR: Four Turyn type sequences of lengths 36, 36,36, 35, 35 are found by a computer search and used to generate a number of new T‐sequences, creating many new Hadamard matrices constructible using these new T-sequences.
Dissertation
On orthogonal matrices
TL;DR: In this paper, Behbahani et al. showed that the OD(l2; 1,1, 1, 9) is the only orthogonal design constructible from 16 circulant matrices, whenever n > 1 is an odd integer, and showed that for each integer n for which 4n is the order of a Hadamard matrix and 8n 2 + 1 is a prime, there is a productive regular matrix of order 16n 2 (8n 2 ) 2.
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A complete description of Golay pairs for lengths up to 100
Peter Borwein,Ron Ferguson +1 more
TL;DR: In extending the theory of composition, this paper is able to obtain a closed formula for the number of pairs of length 2 k n generated by a primitive pair of length n, and identifies five primitive pairs.
References
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Complementary series
TL;DR: These series, which were originally conceived in connection with the optical problem of multislit spectrometry, also have possible applications in communication engineering, for when the two kinds of elements of these series are taken to be +1 and -1, it follows immediately from their definition that the sum of their two respective autocorrelation series is zero everywhere, except for the center term.
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Static multislit spectrometry and its application to the panoramic display of infrared spectra.
TL;DR: The rate at which information about infrared spectra can be obtained in this manner is illustrated by a photograph of the CO2 spectrum which includes both the 14μ and 15μ absorption bands, and which was obtained in 100 milliseconds.
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Quaternary codes for pulsed radar
TL;DR: A class of quaternary codes is described, and an algorithm for generating the codes is given that makes them useful for radar applications.