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On the asymptotic existence of complex Hadamard matrices

✍ Scribed by R. Craigen; W. H. Holzmann; H. Kharaghani

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 159 KB
Volume: 5
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1997)5:5<319::aid-jcd1>3.0.co;2-i

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✦ Synopsis

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 asymptotic existence of Hadamard matrices. We also present a method that gives complex orthogonal designs of order 2 α+ 1 q from complex orthogonal designs of order 2 α . We also demonstrate the existence of a block circulant complex Hadamard matrix of order 2 β q, where β = 4 log 2 (q-1) 10

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