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A note on Hadamard arrays

Published online by Cambridge University Press:  17 April 2009

Joan Cooper
Joan Cooper
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales.
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Let V = mk + 1 be a prime power; we show for m even it is not possible to partition the Galois field GF(v) to give four (0, 1, −1) matrices X1, X2, X3, X4 satisfying:

(i) Xi * Xj = 0, i ≠ j, i, j = 1, 2, 3, 4;

(ii) is a (1, −1) matrix;

(iii) Thus this method of partitioning the Galois field GF(V), into four matrices satisfying the above conditions, cannot be used to find Baumert-Hall Hadamard arrays BH[4V] for v = 9, 11, 17, 23, 27, 29, ….

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 10 , Issue 1 , February 1974 , pp. 15 - 21
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Cooper, Joan, “A binary composition for collections and sets”, Proc. First Austral. Conf. Combinatorial. Math., Newcastle, 1972, 145–161 (TUNRA, Newcastle, 1972).Google Scholar
[2]Cooper, Joan and Wallis, Jennifer, “A construction for Hadamard arrays”, Bull. Austral. Math. Soc. 7 (1972), 269–277.CrossRefGoogle Scholar
[3]Hunt, David C. and Wallis, Jennifer, “Cyclotomy, Hadamard arrays and supplementary difference sets”, Proc. Second Manitoba Conf. Numerical Mathematics, October 1972, 351–381 (Congressus Numerantium, 7. University of Manitoba, Winnipeg, 1972).Google Scholar
[4]Storer, Thomas, Cyclotorny and difference sets (Lectures in Advanced Mathematics, 2. Markham, Chicago, Illinois, 1967).Google Scholar