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Hadamard designs

Published online by Cambridge University Press:  17 April 2009

Jennifer Wallis
Jennifer Wallis
Affiliation:
La Trobe University, Bundoora, Victoria.
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Abstract

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In this paper it is shown that an Hadamard design with each letter repeated once and only once can exist for 2, 4 and 8 letters only.

L.D. Baumert and Marshall Hall, Jr have found a design with four letters each repeated three times. Their design and the design on four letters each repeated once, found by J. Williamson, is the totality previously published.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 1 , February 1970 , pp. 45 - 54
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Baumert, L.D. and Hall, Marshall Jr, “A new construction for Hadamard matrices”, Bull. Amer. Math. Soc. 71 (1965), 169–170.CrossRefGoogle Scholar
[2]Hall, Marshall Jr, Combinatorial theory (Blaisdell Publishing Co. [Ginn & Co.], Waltham, Massachusettes, Toronto, London, 1967).Google Scholar
[3]Wallis, Jennifer, “(v, k,λ)-configurations and Hadamard matrices”, J. Austral. Math. Soc. (to appear).Google Scholar
[4]Williamson, John, “Hadamard's determinant theorem and the sum of four squares”, Duke Math. J. 11 (1944), 65–81.CrossRefGoogle Scholar