Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T01:00:22.304Z Has data issue: false hasContentIssue false
  • English
  • Français

Symmetric Conference Matrices of Order pq2 + 1

Published online by Cambridge University Press:  20 November 2018

Rudolf Mathon
Rudolf Mathon*
Affiliation:
University of Toronto Toronto, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A conference matrix of order n is a square matrix C with zeros on the diagonal and ±1 elsewhere, which satisfies the orthogonality condition CCT = (n — 1)I. If in addition C is symmetric, C =CT, then its order n is congruent to 2 modulo 4 (see [5]). Symmetric conference matrices (C) are related to several important combinatorial configurations such as regular two-graphs, equiangular lines, Hadamard matrices and balanced incomplete block designs [1; 5; and 7, pp. 293-400]. We shall require several definitions.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 321 - 331
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Belevitch, V., Conference networks and Hadamard matrices, Ann. Soc. Scientifique Brux. T. 82 (1968), 13–32.Google Scholar
2. Delsarte, P., An algebraic approach to the association schemes of coding theory, Philips Res. Repts. Suppl. No. 10 (1973).Google Scholar
3. Goethals, J. M., and Seidel, J. J., Orthogonal matrices with zero diagonal, Can. J. Math. 19 (1967), 1001–1010.Google Scholar
4. Mathon, R., 3-class association schemes, Proc. Conf. on Algebraic Aspects of Combinatorics, U. of Toronto (1975), 123–155.Google Scholar
5. Seidel, J. J., A survey of two-graphs, Proc. Int. Coll. Théorie Combinatorie, Ace. Naz. Lincei, Roma (1973).Google Scholar
6. Turyn, R. J., On C-matrices of arbitrary powers, Can. J. Math. 23 (1971), 531–535.Google Scholar
7. Wallis, W. D., Street, A., and Wallis, J., Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices, Lecture Notes in Math. 292 (Springer-Verlag, New York, 1972).Google Scholar