$2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb Z$25

Michael Kiermaier; Matthias Koch; Sascha Kurz

doi:10.3934/amc.2011.5.287

Article Contents

2011, Volume 5, Issue 2: 287-301. Doi: 10.3934/amc.2011.5.287

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$2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb Z$₂₅

1.
Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth

Received: April 2010

Revised: August 2010

Published: May 2011

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Abstract

It is shown that the maximal size of a $2$-arc in the projective Hjelmslev plane over $\mathbb Z$₂₅ is $21$, and the $(21,2)$-arc is unique up to isomorphism. Furthermore, all maximal $(20,2)$-arcs in the affine Hjelmslev plane over $\mathbb Z$₂₅ are classified up to isomorphism.

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Mathematics Subject Classification: Primary: 51C05, 51E21; Secondary: 94B05.

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