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

Matthias Koch; Michael Kiermaier; Sascha Kurz

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

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arxiv 1401.4340 v1 pith:35X3UAIP submitted 2014-01-17 math.CO

Michael Kiermaier , Matthias Koch , Sascha Kurz This is my paper · ORCID

classification math.CO

keywords hjelmslevmathbbmaximalplaneaffinearcsisomorphismprojective

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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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