Complex Hadamard matrices
- 1 January 1973
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 1 (3) , 257-272
- https://doi.org/10.1080/03081087308817024
Abstract
R. J. Turyn introduced complex Hadamard matrices and showed that if there is a complex Hadamard matrix of order c and a real Hadamard matrix of order h> > 1, then there is a real Hadamard matrix of order he. Previously, complex Hadamard matrices were only known for a few small orders and the orders for which symmetric conference matrices were known. These latter are known only to exist for orders which can be written as 1+a2 +b2 where a, b are integers. We give many constructions for new infinite classes of complex Hadamard matrices and show that they exist for orders 306,650, 870,1406,2450 and 3782: for the orders 650, 870, 2450 and 3782, a symmetric conference matrix cannot exist.Keywords
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