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On Good Matrices and Skew Hadamard Matrices

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Algebraic Design Theory and Hadamard Matrices

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 133))

Abstract

In her Ph.D. thesis (Seberry) Wallis described a method using a variation of the Williamson array to find suitable matrices, which we will call good matrices, to construct skew Hadamard matrices. Good matrices were designed to plug into the Seberry–Williamson array to give skew-Hadamard matrices. We investigate the properties of good matrices in an effort to find a new, efficient, method to compute these matrices. We give the parameters of the supplementary difference sets (SDS) which give good matrices for use in the Seberry–Williamson array.

This paper is in final form and no similar paper has been or is being submitted elsewhere.

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Author information

Authors and Affiliations

  1. Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW, 2522, Australia

    Gene Awyzio

  2. SCSSE, Centre for Computer and Information Security Research, Faculty of Engineering and Information Sciences, University of Wollongong, Wollongong, NSW, 2522, Australia

    Jennifer Seberry

Authors
  1. Gene Awyzio
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  2. Jennifer Seberry
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Corresponding author

Correspondence to Jennifer Seberry .

Editor information

Editors and Affiliations

  1. School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona, USA

    Charles J. Colbourn

Additional information

Dedicated to Hadi Kharaghani on the occasion on his 70th birthday

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Awyzio, G., Seberry, J. (2015). On Good Matrices and Skew Hadamard Matrices. In: Colbourn, C. (eds) Algebraic Design Theory and Hadamard Matrices. Springer Proceedings in Mathematics & Statistics, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-319-17729-8_2

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