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

Pages: 287 - 301, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.287       Abstract        References        Full Text (427.0K)       Related Articles

Michael Kiermaier - Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany (email)
Matthias Koch - Institut für Mathematik, Universität Bayreuth, D-95440 Bayreuth, Germany (email)
Sascha Kurz - 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.
Mathematics Subject Classification:  Primary: 51C05, 51E21; Secondary: 94B05.

Received: April 2010;      Revised: August 2010;      Published: May 2011.

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