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A Construction for \(\{0,1,-1\}\) Orthogonal Matrices Visualized

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Combinatorial Algorithms (IWOCA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10765))

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Abstract

Propus is a construction for orthogonal \(\pm 1\) matrices, which is based on a variation of the Williamson array, called the propus array

$$\begin{aligned} \left[ \begin{matrix} A&{} B &{} B &{} D \\ B&{} D &{} -A &{}-B \\ B&{} -A &{} -D &{} B \\ D&{} -B &{} B &{}-A \end{matrix} \right] . \end{aligned}$$

This array showed how a picture made is easy to see the construction method. We have explored further how a picture is worth ten thousand words.

We give variations of the above array to allow for more general matrices than symmetric Williamson propus matrices. One such is the Generalized Propus Array (GP).

Dedicated to the Unforgettable Mirka Miller

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Authors and Affiliations

  1. Saint Petersburg State University of Aerospace Instrumentation, 67, B. Morskaia Street, 190000, St. Petersburg, Russian Federation

    N. A. Balonin

  2. School of Computing and Information Technology, EIS, University of Wollongong, Wollongong, NSW, 2522, Australia

    Jennifer Seberry

Authors
  1. N. A. Balonin
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  2. Jennifer Seberry
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Correspondence to Jennifer Seberry .

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Editors and Affiliations

  1. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Ljiljana Brankovic

  2. University of Newcastle Australia, Callaghan, New South Wales, Australia

    Joe Ryan

  3. McMaster University, Hamilton, Ontario, Canada

    William F. Smyth

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Balonin, N.A., Seberry, J. (2018). A Construction for \(\{0,1,-1\}\) Orthogonal Matrices Visualized. In: Brankovic, L., Ryan, J., Smyth, W. (eds) Combinatorial Algorithms. IWOCA 2017. Lecture Notes in Computer Science(), vol 10765. Springer, Cham. https://doi.org/10.1007/978-3-319-78825-8_5

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  • DOI: https://doi.org/10.1007/978-3-319-78825-8_5

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  • Online ISBN: 978-3-319-78825-8

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