Skip to main content
Log in

Maximal arcs in Desarguesian planes of odd order do not exist

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

Forq an odd prime power, and 1<n<q, the Desarguesian planePG(2,q) does not contain an(nq−q+n,n)-arc.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Cossu: Su alcune proprietà dei {k; n}-archi di un piano proiettivo sopra un corpo finito,Rend. Mat. e Appl.,20 (1961), 271–277.

    Google Scholar 

  2. R. H. F. Denniston: Some maximal arcs in finite projective planes,J. Combin. Theory,6 (1969), 317–319.

    Google Scholar 

  3. T. Penttila andG. F. Royle: Sets of type (m, n) in the Affine and Projective Planes of Order Nine,Designs, Codes and Cryptography,6 (1995), 229–245.

    Google Scholar 

  4. L. Rédei: Lückenhafte Polynome über endlichen Körpern, Birkhäuser Verlag, Basel (1970) (English translation: Lacunary polynomials over finite fields, North Holland, Amsterdam, 1973).

    Google Scholar 

  5. J. A. Thas: Construction of maximal arcs and partial geometries,Geom. Dedicata,3 (1974), 61–64.

    Google Scholar 

  6. J. A. Thas: Some results concerning {(q+1)(n−1);n}-arcs and {(q+1)(n−1)+1;n}-arcs in finite projective planes of orderq, J. Combin. Theory Ser. A,19 (1975), 228–232.

    Google Scholar 

  7. J. A. Thas: Construction of maximal arcs and dual ovals in translation planes,Europ. J. Combinatorics,1 (1980), 189–192.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by Italian M.U.R.S.T. (Research Group onStrutture geometriche, combinatoria, loro applicazioni) and G.N.S.A.G.A. of C.N.R.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ball, S., Blokhuis, A. & Mazzocca, F. Maximal arcs in Desarguesian planes of odd order do not exist. Combinatorica 17, 31–41 (1997). https://doi.org/10.1007/BF01196129

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01196129

Mathematics Subject Classification (1991)

Navigation