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Quasi Clifford algebras and systems of orthogonal designs

Part of: Designs and configurations Basic linear algebra

Published online by Cambridge University Press:  09 April 2009

H. M. Gastineau-Hills
H. M. Gastineau-Hills
Affiliation:
Department of Mathematics, University of Sydney, Sydney, NSW 2006, Australia
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Abstract

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The representation theory of Clifford algebras has been used to obtain information on the possible orders of amicable pairs of orthogonal designs on given numbers of variables. If, however, the same approach is tried on more complex systems of orthogonal designs, such as product designs and amicable triples, algebras which properly generalize the Clifford algebras are encountered. In this paper a theory of such generalizations is developed and applied to the theory of systems of orthogonal designs, and in particular to the theory of product designs.

MSC classification

Secondary: 15A66: Clifford algebras, spinors 05B15: Orthogonal arrays, Latin squares, Room squares
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 1 - 23
Copyright
Copyright © Australian Mathematical Society 1982

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