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An infinite class of Hadamard matrices

Part of: Design of experiments Designs and configurations

Published online by Cambridge University Press:  09 April 2009

Christos Koukouvinos  and
Stratis Kounias
Christos Koukouvinos
Affiliation:
Department of Mathematics, University of Thessaloniki, Thessaloniki, Greece54006
Stratis Kounias
Affiliation:
Department of Mathematics, University of Thessaloniki, Thessaloniki, Greece54006
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Abstract

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An infinite class of T-matrices is constructed using Golay sequences. A list is given with new Hadamard matrices of order 2t. q, q odd, q < 10000, improving the known values of t.

Finally T-matrices are given of order 2m + 1, for small values of m ≤ 12 which do not coincide with those generated by Turyn sequences.

Keywords

T-matricesGolay sequencesTuryn sequencesWilliamson typeBaumert-Hall arrays.

MSC classification

Secondary: 62K05: Optimal designs 62K10: Block designs 05B20: Matrices (incidence, Hadamard, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 46 , Issue 3 , June 1989 , pp. 384 - 394
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Agayan, S. S. and Sarukhanyan, A. G., ‘Recurrence formulas for the construction of Williamson-type matrices’, Math. Notes 30 (1982), 796–804.CrossRefGoogle Scholar
[2]Baumert, L. D. and Hall, M. Jr, ‘A new construction for Hadamard matrices’, Bull. Amer. Math. Soc. 71 (1965), 169–170.CrossRefGoogle Scholar
[3]Cooper, J. and Wallis, J., ‘A construction for Hadamard arrays’, Bull. Austral. Math. Soc. 7 (1972), 269–277.CrossRefGoogle Scholar
[4]Geramita, A. V. and Seberry, J., Orthogonal designs: quadratic forms and Hadamard matrices, Marcel Dekker, New York and Basel, 1979.Google Scholar
[5]Ono, T. and Sawade, K., ‘A construction of Baumert-Hall-Welch array of order 36’, Sugaku 36 (1984), 172–174. (in Japanese)Google Scholar
[6]Sawade, K., ‘A Hadamard matrix of order 268’, Graphs and Combinatorics 1 (1985), 185–187.CrossRefGoogle Scholar
[7]Seberry, J., ‘A computer listing of Hadamard matrices’, Proceedings of the International Conference on Combinatorial Mathematics, Canberra, (Lecture Notes in Math., vol. 686, Springer-Verlag, Berlin-Heidelberg-New-York, 1977, pp. 275–281).CrossRefGoogle Scholar
[8]Seberry, J., Private communication (1985).Google Scholar
[9]Seberry, J., ‘A new construction for Williamson-type matrices’, Graphs and Combinatorics 2 (1986), 81–87.CrossRefGoogle Scholar
[10]Wallis, J. Seberry, ‘On Hadamard matrices’, J. Combinatorial Theory Ser. A 18 (1975), 149–164.CrossRefGoogle Scholar
[11]Wallis, J. Seberry, ‘On the existence of Hadamard matrices’, J. Combinatorial Theory Ser. A 21 (1976), 444–451.CrossRefGoogle Scholar
[12]Turyn, R. J., ‘Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings’, J. Combinatorial Theory Ser. A 16 (1974), 313–333.CrossRefGoogle Scholar
[13]Yamada, M., ‘Some new series of Hadamard matrices’, Proc. Japan Academy Ser. A 63 (1987), 86–89.CrossRefGoogle Scholar
[14]Yamada, M., ‘Hadamard matrices generated by an adaptation of generalized quaternion type array’, Graphs and Combinatorics 2 (1986), 179–187.CrossRefGoogle Scholar
[15]Yang, C. H., ‘Hadamard matrices and δ-codes of length 3n’, Proc. Amer. Math. Soc. 85 (1982), 480–482.Google Scholar
[16]Yang, C. H., ‘Lagrange identify for polynomials and δ-codes of lengths 7t and 13t’, Proc. Amer. Math. Soc. 88 (1983), 746–750.Google Scholar
[17]Yang, C. H., ‘A composition theorem for δ-codes’, Proc. Amer. Math. Soc. 89 (1983), 375–378.Google Scholar