Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-14T11:16:37.437Z Has data issue: false hasContentIssue false
  • English
  • Français

On the structure and existence of some amicable orthogonal designs

Part of: Designs and configurations Design of experiments

Published online by Cambridge University Press:  09 April 2009

Peter J. Robinson  and
Jennifer Seberry
Peter J. Robinson
Affiliation:
Institute of Advanced Studies Australian National UniversityCanberra
Jennifer Seberry
Affiliation:
Department of Applied Mathementics The University of Sydney
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.

The structure is determined for the existence of some amicable weighing matrices. This is then used to prove the existence and non-existence of some amicable orthogonal designs in powers of two.

MSC classification

Secondary: 05B20: Matrices (incidence, Hadamard, etc.) 62K99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 25 , Issue 1 , February 1978 , pp. 118 - 128
Copyright
Copyright © Australian Mathematical Society 1978

References

Delsarte, P., Goethals, J. M. and Seidel, J. J. (1971), “Orthogonal matrices with zero diagonal. II”, Canad. J. Math. 23, 816–832.CrossRefGoogle Scholar
Geramita, A. V., Geramita, J. Murphy and Wallis, J. Seberry (1975–1976), “Orthogonal designs” Linear and Multilinear Algebra 3, 281–306.CrossRefGoogle Scholar
Geramita, A. V. and Verner, J. H. (1976), “Orthogonal designs with zero diagonal”, Canad. J. Math. 28, 215–224.CrossRefGoogle Scholar
Robinson, P. J. (1976)a, “Amicable orthogonal designs”, Bull. Austral. Math. Soc. 14, 303–314.CrossRefGoogle Scholar
Robinson, P. J. (1976b), “A non-existence theorem for orthogonal designs”, Utilitas Math. 10, 179–184.Google Scholar
Robinson, P. J. (1977a), “Using product designs to construct orthogonal designs”, Bull. Austral. Math. Soc. 16, 297–305.CrossRefGoogle Scholar
Robinson, P. J. (1977b), “Concerning the existence and construction of orthogonal designs”, Ph.D. Thesis, Australian National University, Canberra.CrossRefGoogle Scholar
Robinson, P. J. and Seberry, J. (to appear), “Orthogonal designs in powers of two”, Ars Combinatoria.Google Scholar
Shapiro, D. (1975–1976) (private communication).Google Scholar
Wallis, J. Seberry (1975), “Constructions for amicable orthogonal designs”, Bull. Austral. Math. Soc. 12, 179–182.CrossRefGoogle Scholar
Seberry, J. Wallis and Whiteman, A. L. (1975), “Some results on weighing matrices”, Bull. Austral. Math. Soc. 12, 433–477.Google Scholar
Wolfe, W. W. (to appear), “Rational quadratic forms and orthogonal designs”, J. Number Theory.Google Scholar
Wolfe, W. W. (1976), ‘Amicable orthogonal designs—existence”, Canad. J. Math., 28, 1006–1020.CrossRefGoogle Scholar
Wolfe, W. W. (1975), “Orthogonal designs—amicable orthogonal designs—some algebraic and combinatorial techniques”, Ph.D. Dissertation, Queen's University, Kingston, Ontario.Google Scholar