Abstract
We classify the arcs in $\mathrm{PG}(2,q)$, $q$ odd, which consist of $(q+3)/2$ points of a conic $C$ and two points not on te conic but external to $C$, or $(q+1)/2$ points of $C$ and two additional points, at least one of which is an internal point of $C$. We prove that for arcs of the latter type, the number of points internal to $C$ can be at most $4$, and we give a complete classification of all arcs that attain this bound. Finally, we list some computer results on extending arcs of both types with further points.
Publisher
The Electronic Journal of Combinatorics
Subject
Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science,Applied Mathematics,Discrete Mathematics and Combinatorics
Cited by
3 articles.
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