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A construction for Hadamard arrays

Published online by Cambridge University Press:  17 April 2009

Joan Cooper  and
Jennifer Wallis
Joan Cooper
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales.
Jennifer Wallis
Affiliation:
Department of Mathematics, University of Newcastle, New South Wales.
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Abstract

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We give a construction for Hadamard arrays and exhibit the arrays of orders 4t, t ∈ {1, 3, 5, 7, …, 19}. This gives seventeen new Hadamard matrices of order less than 4000.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 2 , October 1972 , pp. 269 - 277
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Baumert, Leonard D., Cyclic difference sets (Lecture Notes in Mathematics, 182. Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[2]Baumert, L.D. and Hall, Marshall, Jr, “A new construction for Hadamard matrices” Bull. Amer. Math. Soc. 71 (1965), 169–170.CrossRefGoogle Scholar
[3]Goethals, J.M. and Seidel, J.J., “A skew Hadamard matrix of order 36 “, J. Austral. Math. Soc. 11 (1970), 343–344.CrossRefGoogle Scholar
[4]Hall, Marshall Jr, Combinatorial theory (Blaisdell Publishing Co. [Ginn & Co.], Waltham, Massachusetts; Toronto; London; 1967).Google Scholar
[5]Turyn, Richard J., “An infinite class of Williamson matrices” J. Combinatorial Theory 12 (1972), 319–321.CrossRefGoogle Scholar
[6]Wallis, Jennifer, “Hadamard matrices of order 28m, 36m and 44m”, J. Combinatorial Theory (to appear).Google Scholar
[7]Wallis, Jennifer, “On supplementary difference sets” Aequationes Math, (to appear).Google Scholar
[8]Wallis, Jennifer, “A note on BIBDs” J. Austral. Math. Soc. (to appear).Google Scholar
[9]Whiteman, Albert Leon, “An infinite family of skew Hadamard matrices” (to appear).Google Scholar
[10]Williamson, John, “Hadamard's determinant theorem and the sum of few squares” Duke J. Math. 11 (1944), 65–81.CrossRefGoogle Scholar