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On the matrices used to construct baumert-hall arrays

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Combinatorial Mathematics III

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 452))

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Abstract

Four circulant (or type 1) (0,1,−1) matrices X1, X2, X3, X4 of order t with the property that each of the t2 positions is non-zero in precisely one of the Xi and such that

$$X_1 X_1 ^T + X_2 X_2 ^T + X_3 X_3 ^T + X_4 X_4 ^T = tI_t$$

will be called T-matrices.

This paper studies the construction, use and properties of T-matrices giving a new construction for Hadamard matrices and some new equivalence results for Hadamard matrices and Baumert-Hall arrays.

Written while this author was visiting the Mathematics Department, S.U.N.Y. at Buffalo, New York.

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Author information

Authors and Affiliations

  1. Department of Mathematics, State University of New York at Buffalo, Amherst, New York, USA

    Richard B. Lakein & Jennifer Seberry Wallis

  2. Department of Pure Mathematics Institute of Advanced Studies, Australian National University, Canberra

    Richard B. Lakein & Jennifer Seberry Wallis

Authors
  1. Richard B. Lakein
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  2. Jennifer Seberry Wallis
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Editor information

Anne Penfold Street Walter Denis Wallis

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© 1975 Springer-Verlag

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Lakein, R.B., Wallis, J.S. (1975). On the matrices used to construct baumert-hall arrays. In: Street, A.P., Wallis, W.D. (eds) Combinatorial Mathematics III. Lecture Notes in Mathematics, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069554

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  • DOI: https://doi.org/10.1007/BFb0069554

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07154-9

  • Online ISBN: 978-3-540-37482-4

  • eBook Packages: Springer Book Archive

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