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An Algorithm for Constructing Hjelmslev Planes

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Algebraic Design Theory and Hadamard Matrices

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

Abstract

Projective Hjelmslev planes and affine Hjelmslev planes are generalisations of projective planes and affine planes. We present an algorithm for constructing projective Hjelmslev planes and affine Hjelmslev planes that uses projective planes, affine planes and orthogonal arrays. We show that all 2-uniform projective Hjelmslev planes and all 2-uniform affine Hjelmslev planes can be constructed in this way. As a corollary it is shown that all 2-uniform affine Hjelmslev planes are sub-geometries of 2-uniform projective Hjelmslev planes.

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Acknowledgements

Thanks to Jesse Waechter-Cornwill for the coding and visualisation of Algorithm 4.1. Thanks are due to Cathy Baker for highlighting reference [10].

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Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD, 4000, Australia

    Joanne L. Hall

  2. School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC, 3001, Australia

    Asha Rao

Authors
  1. Joanne L. Hall
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  2. Asha Rao
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Corresponding author

Correspondence to Asha Rao .

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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Hall, J.L., Rao, A. (2015). An Algorithm for Constructing Hjelmslev Planes. 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_11

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