Non-free extensions of the simplex codes over a chain ring with four elements

Honold, Thomas; Landjev, Ivan

doi:10.1007/s10623-012-9649-7

Cited by 2 publications

(2 citation statements)

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“…e-mail: j42.hall@qut.edu.au Asha Rao School of Mathematical and Geospatial Sciences, RMIT University. e-mail: asha@rmit.edu.au ring Hjelmslev geometries [12,14,15], though there has been some more recent work using other chain rings [11,13].…”

Section: Introductionmentioning

confidence: 99%

“…A difficulty turns out to be explicit constructions and concrete examples, which would help further investigations. Some Hjelmslev planes can be constructed using chain rings [20], those that have been the most thoroughly investigated have been the Galois ring Hjelmslev geometries [12,14,15], though there has been some more recent work using other chain rings [11,13].…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm for Constructing Hjelmslev Planes

Hall

Rao

2015

Springer Proceedings in Mathematics &Amp; Statistics

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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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