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On Generalized k-Arcs in
B.N.cooperstein1and J.A.Thas2
1Department of Mathematics, University of California, Santa Cruz, CA 95064, USA
2Department of Pure Mathematics and Computer Algebra, Ghent University, Belgium
Annals of Combinatorics 5(2) p.141-152 June, 2001
AMS Subject Classification: 05E20, 20B25, 51E14, 94B27
The notion of a generalized k-arc in is introduced. When demonstrated that the existence of a generalized k-arc in leads to a construction of a partial geometry, a strongly regular graph and a two-weight code. Such k-arcs are called generalized hyperovals. It is proved that no such generalized hyperovals exist when q is odd. For each and q = 2 it is shown that each generalized hyperoval of is a partition of \. Related structures are also discussed.
Keywords: projective space, k-arc, oval, hyperoval, strongly regular graph, partial geometry, two-weight code


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