$2$-arcs of maximal size in the affine and the projective Hjelmslev plane over $\mathbb Z$25
Michael Kiermaier - Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany (email)
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.
Keywords: Hjelmslev geometry, arc, nite chain ring, Galois ring.
Received: April 2010; Revised: August 2010; Published: May 2011.
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