Sets of Type (d 1,d 2) in Projective Hjelmslev Planes over Galois Rings

Axel Kohnert ()
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Axel Kohnert: University of Bayreuth, Mathematisches Institut

A chapter in Algorithmic Algebraic Combinatorics and Gröbner Bases, 2009, pp 269-278 from Springer

Abstract: 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.

Keywords: Projective Hjelmslev plane; Two-weight codes; Arcs (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-01960-9_9

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DOI: 10.1007/978-3-642-01960-9_9

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