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2015 | OriginalPaper | Chapter

An Algorithm for Constructing Hjelmslev Planes

Authors : Joanne L. Hall, Asha Rao

Published in: Algebraic Design Theory and Hadamard Matrices

Publisher: Springer International Publishing

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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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previous chapter On Symmetric Designs and Binary 3-Frameproof Codes

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Title: An Algorithm for Constructing Hjelmslev Planes
Authors: Joanne L. Hall
Asha Rao
Publisher: Springer International Publishing
Book: Algebraic Design Theory and Hadamard Matrices
Print ISBN: 978-3-319-17728-1

Electronic ISBN: 978-3-319-17729-8

Copyright Year: 2015
DOI: https://doi.org/10.1007/978-3-319-17729-8_11

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