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Trace, Symmetry and Orthogonality

Published online by Cambridge University Press:  20 November 2018

R. Craigen
R. Craigen*
Affiliation:
Department of Mathematics and Computer Science, University of Lethbridge Lethbridge, Alberta T1K 3M4 email:, craigen@cs.uleth.ca
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Abstract

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Does there exist a circulant conference matrix of order > 2? When is there a symmetric Hadamard matrix with constant diagonal? How many pairwise disjoint, amicable weighing matrices of order n can there be? These are questions concerning which the trace function gives a great deal of insight. We offer easy proofs of the known solutions to the first two, the first being new, and develop new results regarding the latter question. It is shown that there are 2t disjoint amicable weighing matrices of order 2tp, where p is odd, and that this is an upper bound for t ≤ 1. An even stronger bound is obtained for certain cases.

Keywords

Primary: 05B20secondary: 15A1505C50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 461 - 467
Copyright
Copyright © Canadian Mathematical Society 1994

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