Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-25T01:33:26.808Z Has data issue: false hasContentIssue false
  • English
  • Français

Amicable Orthogonal Designs-Existence

Published online by Cambridge University Press:  20 November 2018

Warren Wolfe
Warren Wolfe*
Affiliation:
University of Alberta, Edmonton, Alberta
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.

Definition. An orthogonal design in order n and of type (u1, … , us) on the commuting variables x1, . . . , xs is an n X n matrix, X, with entries from the set ﹛0, ±x1, … , ±xs﹜ such that

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 5 , 01 October 1976 , pp. 1006 - 1020
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Adams, J. F., Lax, P. D., and Phillips, J. S., On matrices whose real linear co?nbinations are non-singular, Proc. A.M.S. 16 (1965), 318–322.Google Scholar
2. Clifford, W. K., Applications of Grassmans extensive algebra. Amer. J. Math. 1 (1878), 350- 358.Google Scholar
3. Geramita, A. V., and Pullman, N. J., A theorem of Hurwitz and Radon and orthogonal projective modules, Proc. A.M.S. 42 (1974), 51–58.Google Scholar
4. Geramita, A. V., Geramita, J. M., and Wallis, J. S., Orthogonal designs, to appear, Journal of Linear and Multilinear Algebra.Google Scholar
5. Kawada, Y., and Iwahori, N., On the structure and representations of Clifford algebra, J. Math. Soc. Japan 2 (1950), 34–43.Google Scholar
6. Lam, T. Y., The algebraic theory of quadratic forms, Math. Lecture Notes Series (Benjamin, Reading, Mass., 1973).Google Scholar
7. Shapiro, Dan, Rational spaces of similarities, unpublished.Google Scholar
8. Shapiro, Dan, Spaces of similarities I: the Hurwitz problem, pre-print.Google Scholar
9. Shapiro, Dan, Spaces of similarities IV: (s, t) families, pre-print.Google Scholar
10. Witt, E., Théorie der quadratischen Formen in beliebigen Korpern, Crellee J. 176 (1937), 31–44.Google Scholar
11. Wolfe, W., Rational quadratic forms and orthogonal designs, to appear, J. Number Theory.Google Scholar