Sets of Type (d1,d2) in Projective Hjelmslev Planes over Galois Rings

Chapter

Summary

In this paper we construct sets of type (d 1,d 2) in the projective Hjelmslev plane. For computational purposes we restrict ourself to planes over \( {\mathbb{Z}_{{p^s}}} \) with p a prime and s>1, but the method is described over general Galois rings. The existence of sets of type (d 1,d 2) is equivalent to the existence of a solution of a Diophantine system of linear equations. To construct these sets we prescribe automorphisms, which allows to reduce the Diophantine system to a feasible size. At least two of the newly constructed sets are ‘good’ u-arcs. The size of one of them is close to the known upper bound.

Key words

Projective Hjelmslev plane Two-weight codes Arcs 

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversity of BayreuthBayreuthGermany

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