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On the real unbiased Hadamard matrices. (English) Zbl 1231.05043
Brualdi, Richard A. (ed.) et al., Combinatorics and graphs. Selected papers based on the presentations at the 20th anniversary conference of IPM on combinatorics, Tehran, Iran, May 15–21, 2009. Dedicated to Reza Khosrovshahi on the occasion of his 70th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4865-4/pbk). Contemporary Mathematics 531, 243-250 (2010).
Summary: The class of mutually unbiased Hadamard (MUH) matrices is studied. We show that the number of MUH matrices of order \(4n^2\), \(n\) odd is at most \(2\) and that the bound is attained for \(n= 1,3\). Furthermore, we find a lower bound for the number of MUH matrices of order \(16n^2\), assuming the existence of a Hadamard matrix of order \(4n\). An extension to unbiased weighing matrices is also presented.
For the entire collection see [Zbl 1202.05003].

05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)