Skip to main content
Log in

Normal Rational Curves Over Prime Fields

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

It is shown that in the projective spaces PG(n,p),p prime, 2 ≤ np-2, the normal rational curves are the only (p+1)-arcs fixed by a projective group G isomorphic to PSL(2,p).

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.

Similar content being viewed by others

References

  1. L.R.A. Casse and D.G. Glynn, The solution to Beniamino Segre's problem I r,qr = 3, q = 2h, Geom. Dedicata, Vol. 13 (1982) pp. 157–163.

    Google Scholar 

  2. D.G. Glynn, The non-classical 10-arc of PG(4,9), Discrete Math., Vol. 59 (1986) pp. 43–51.

    Google Scholar 

  3. J.W.P. Hirschfeld, Finite Projective Spaces of Three Dimensions, Clarendon Press, Oxford (1985).

    Google Scholar 

  4. J.W.P. Hirschfeld and J.A. Thas, General Galois Geometries, Oxford University Press, Oxford (1991).

    Google Scholar 

  5. F.J. MacWilliams and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam (1977).

    Google Scholar 

  6. C.M. O'Keefe and L. Storme, Arcs fixed by A 5 and A 6, J. Geom., Vol. 55 (1996) pp. 123–138.

    Google Scholar 

  7. L. Storme and J.A. Thas, Complete k-arcs in PG(n,q), q even, Discrete Math., Vol. 106/107 (1992) pp. 455–469.

    Google Scholar 

  8. L. Storme and J.A. Thas, k-Arcs and dual k-arcs, Discrete Math., Vol. 125 (1994) pp. 357–370.

    Google Scholar 

  9. L. Storme and H. Van Maldeghem, Cyclic arcs in PG(2, q), J. Algebraic Combin., Vol. 3 (1994) pp. 113–128.

    Google Scholar 

  10. L. Storme and H. Van Maldeghem, Arcs fixed by a large cyclic group, Atti Sem. Mat. Fis. Univ. Modena, Vol. XLIII (1995) pp. 273–280.

    Google Scholar 

  11. L. Storme and H. Van Maldeghem, Primitive arcs in PG(2, q), J. Combin. Theory. Series A, Vol. 69 (1995) pp. 200–216.

    Google Scholar 

  12. J.A. Thas, Normal rational curves and k-arcs in Galois spaces, Rend. Mat., Vol. 1 (1968) pp. 331–334.

    Google Scholar 

  13. J.F. Voloch, Arcs in projective planes over prime fields, J. Geom., Vol. 38 (1990) pp. 198–200.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Storme, L. Normal Rational Curves Over Prime Fields. Designs, Codes and Cryptography 12, 89–96 (1997). https://doi.org/10.1023/A:1008202127766

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008202127766

Navigation