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The excess of complex Hadamard matrices

✍ Scribed by H. Kharaghani; Jennifer Seberry

Publisher: Springer Japan
Year: 1993
Tongue: English
Weight: 358 KB
Volume: 9
Category: Article
ISSN: 0911-0119
DOI: 10.1007/bf01195326

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📜 SIMILAR VOLUMES

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✍ Nikos Farmakis; Stratis Kounias 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 542 KB

Hadamard matrices of order n with maximum excess o(n) are constructed for n = 40, 44, 48, 52, 80, 84. The results are: o(40)= 244, o(44)= 280, o(48)= 324, o(52)= 364, o(80)= 704, 0(84) = 756. A table is presented listing the known values of o(n) 0< n ~< 100 and the corresponding Hadamard matrices ar

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We show that if there is a skew-Hadamard matrix of order m then there is an Hadamard matrix of order 4m2 -4m whose excess attains the maximum possible bound predicted by S. Kounias and N. Farmakis, On the excess of Hadamard matrices, Discrete Mathematics 68 (1988) 59-69. That is a(4m\* -4m) = 4(m -1

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Let N = N (q) be the number of nonzero digits in the binary expansion of the odd integer q. A construction method is presented which produces, among other results, a block circulant complex Hadamard matrix of order 2 α q, where α ≥ 2N -1. This improves a recent result of Craigen regarding the asympt

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✍ R. Craigen; H. Kharaghani 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 165 KB

## Abstract Weaving is a matrix construction developed in 1990 for the purpose of obtaining new weighing matrices. Hadamard matrices obtained by weaving have the same orders as those obtained using the Kronecker product, but weaving affords greater control over the internal structure of matrices co