Sets of Type (d1,d2) in projective Hjelmslev planes over Galois Rings
Axel
Kohnert
;
Springer,
in:
Doi-Nummer:
Abstract:
In this paper we construct sets of type (d1, d2) in the projective Hjelmslev plane.
For computational purposes we restrict ourself to planes over Zps with p a prime and s > 1,
but the method is described over general Galois rings. The existence of sets of type (d1, d2)
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.
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