University of Sussex
Browse

File(s) not publicly available

Arcs and curves over a finite field

journal contribution
posted on 2023-06-07, 20:41 authored by J W P Hirschfeld, G Korchmáros
In [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 Applications

ISSN

1071-5797

Publisher

Elsevier

Issue

4

Volume

5

Page range

393-408

ISBN

1071-5797

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

Usage metrics

    University of Sussex (Publications)

    Categories

    No categories selected

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC