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Construction of some new Hadamard matrices

Published online by Cambridge University Press:  17 April 2009

Dragomir Ž. Đoković
Affiliation:
Department of Pure MathematicsUniversity of Waterloo Waterloo, OntarioCanadaN2L 3G1
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Abstract

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We prove that there exist skew type Hadamard matrices of order 4n for n = 67, 113, 127, 157, 163, 181 and 241 which have not been constructed so far. In particular there exists a Hadamard matrix of order 4 · 163, which was unknown until now. We mention that very recently we have constructed skew type Hadamard matrices of orders 4n for n = 37 and 43.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Đoković, D. Ž., ‘Skew Hadamard matrices of order 4 · 37 and 4 · 43’, J. Combin. Theory Ser. A (to appear).Google Scholar
[2]Geramita, A. and Seberry, J., Orthogonal Designs (M. Dekker, New York – Basel, 1979).Google Scholar
[3]Sawade, K., ‘A Hadamard matrix of order 268’, Graphs Combin. 1 (1985), 185187.CrossRefGoogle Scholar
[4]Wallis, J. Seberry, ‘Hadamard matrices, Part FV’, in Combinatorics: Room squares, sum free sets, Hadamard matrices 292: Lecture Notes in Mathematics, by Wallis, W.D., Street, A. Penfold, Wallis, J. Seberry (Springer-Verlag, Berlin, Heidelberg, New York, 1972).CrossRefGoogle Scholar
[5]Seberry, J., ‘On skew Hadamard matrices’, Ars Combin. 6 (1978), 255275.Google Scholar
[6]Szekeres, G., ‘A note on skew type orthogonal ±1 matrices’, in Combinatorics: Colloq. Math. Soc. János Bolyai, Editors Hajnal, A., Lovász, L., and Sós, V. T., pp. 489498 (North Holland, 1988).Google Scholar
[7]Yamada, M., ‘Some new series of Hadamard matrices’, J. Austral. Math. Soc. Ser. A 46 (1989), 371383.CrossRefGoogle Scholar