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Orthogonal Matrices with Zero Diagonal. II

Published online by Cambridge University Press:  20 November 2018

P. Delsarte ,
J. M. Goethals  and
J. J. Seidel
P. Delsarte
Affiliation:
M.B.L.E. Research Laboratory, Brussels, Belgium;
J. M. Goethals
Affiliation:
M.B.L.E. Research Laboratory, Brussels, Belgium;
J. J. Seidel
Affiliation:
Technological University, Eindhoven, Netherlands
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C-matrices appear in the literature at various places; for a survey, see [11]. Important for the construction of Hadamard matrices are the symmetric C-matrices, of order v ≡ 2 (mod 4), and the skew C-matrices, of order v ≡ 0 (mod 4). In § 2 of the present paper it is shown that there are essentially no other C-matrices. A more general class of matrices with zero diagonal is investigated, which contains the C-matrices and the matrices of (v, k, λ)-systems on k and k + 1 in the sense of Bridges and Ryser [6]. Skew C-matrices are interpreted in § 3 as the adjacency matrices of a special class of tournaments, which we call strong tournaments. They generalize the tournaments introduced by Szekeres [24] and by Reid and Brown [21].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 5 , October 1971 , pp. 816 - 832
Copyright
Copyright © Canadian Mathematical Society 1971

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