On Generalized *k*-Arcs in

B.N.cooperstein^{1}and J.A.Thas^{2}

Annals of Combinatorics 5(2) p.141-152 June, 2001

Abstract:

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.

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