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Arcs and curves over a finite field
journal contribution
posted on 2023-06-07, 20:41 authored by J W P Hirschfeld, G KorchmárosIn [11], a new bound for the number of points on an algebraic curve over a finite field of odd order was obtained, and applied to improve previous bounds on the size of a complete arc not contained in a conic. Here, a similar approach is used to show that a complete arc in a plane of even order q has size q+2 or View the MathML source or less than View the MathML source. To obtain this result, first a new characterization of a Hermitian curve for any square q is given; more precisely, it is shown that a curve of sufficiently low degree has a certain upper bound for the number of its rational points with equality occurring in this bound only when the curve is Hermitian. Finally, another application is given concerning the degree of the curve on which a unital can lie.
History
Publication status
- Published
Journal
Finite Fields and Their ApplicationsISSN
1071-5797Publisher
ElsevierExternal DOI
Issue
4Volume
5Page range
393-408ISBN
1071-5797Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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