Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-22T04:33:29.431Z Has data issue: false hasContentIssue false
  • English
  • Français

On a problem of K. A. Bush concerning Hadamard matrices

Published online by Cambridge University Press:  17 April 2009

W.D. Wallis
W.D. Wallis
Affiliation:
The University of Newcastle, Newcastle, New South Wales.
Rights & Permissions [Opens in a new window]

Abstract

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.

K.A. Bush has asked whether there is a symmetric Hadamard matrix of order m2, m even, which can be partitioned into an m × m array of m × m blocks, such that:

(i) each diagonal block has every entry 1;

(ii) each non-diagonal block has every row-sum zero?

We give two ways of constructing such matrices.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 3 , June 1972 , pp. 321 - 326
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Bose, R.C. and Shrikhande, S.S., “Graphs in which each pair of vertices is adjacent to the same number d of other vertices”, Studia Sci. Math. Hungar. 5 (1970), 181–195.Google Scholar
[2]Bruck, R.H., “Finite nets, II. Uniqueness and imbedding”, Pacific J. Math. 13 (1963), 421–457.CrossRefGoogle Scholar
[3]Bush, K.A., “An inner orthogonality of Hadamard matrices”, J. Austral. Math. Soc. 12 (1971), 242–248.CrossRefGoogle Scholar
[4]Bush, K.A., “Unbalanced Hadamard matrices and finite projective planes of even order”, J. Combinatorial Theory Ser. A 11 (1971), 38–44.CrossRefGoogle Scholar
[5]Guy, Richard, Hanani, Haim, Sauer, Norbert and Schönheim, Johanan, (Editors), Combinatorial structures and their applications. Proc. Calgary Internat. Conf. Univ. Calgary, Calgary, Alberta, 1969. (Gordon and Breach, New York, London, Paris, 1970).Google Scholar
[6]Hall, Marshall Jr, Combinatorial theory (Blaisdell Publishing Co. [Ginn and Co.], Waltham, Massachusetts; Toronto, Ontario; London; 1967).Google Scholar
[7]Wallis, W.D., “Certain graphs arising from Hadamard matrices”, Bull. Austral. Math. Soc. 1 (1969), 325–331.CrossRefGoogle Scholar
[8]Wallis, W.D., “Construction of strongly regular graphs using affine designs”, Bull. Austral. Math. Soc. 4 (1971), 41–49.CrossRefGoogle Scholar
[9]Wallis, W.D., “Construction of strongly regular graphs using affine designs: Corrigenda”, Bull. Austral. Math. Soc. 5 (1971). 431.CrossRefGoogle Scholar
[10]Wallis, W.D., “Special Hadamard matrices”, Abstract, to appear in Notices Amer. Math. Soc. 19 (1972).Google Scholar