Skip to main content
Log in

On multi-Frobenius non-classical plane curves

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

In this paper, we characterize the plane curves over \({\mathbb {F}_q}\) which are Frobenius non-classical for different powers of q.

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. Borges H.: On complete (N, d)-arcs derived from plane curves. Finite Fields Appl. 15, 82–96 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  2. Garcia A.: The curves y n = f(x) over finite fields. Arch. Math. 54, 36–44 (1990)

    Article  MATH  Google Scholar 

  3. van der Geer G., van der Vlugt M.: Tables of curves with many points. Math. Comput. 69, 797–810 (2000)

    MATH  Google Scholar 

  4. Giullietti M. et al.: On complete arcs arising from plane curves. Des. Codes Cryptogr. 25, 237–246 (2002)

    Article  MathSciNet  Google Scholar 

  5. R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer, New York, 1977, xvi+496pp.

  6. Hefez A., Voloch J.F.: Frobenius non classical curves. Arch. Math. 54, 263–273 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  7. Hirschfeld J.W.P., Korchmáros G.: On the number of solutions of an equation over a finite field. Bull. London Math. Soc. 33, 16–24 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  8. Stohr K.-O., Voloch J.F.: Weierstrass Points and Curves over Finite Fields. Proc. London Math. Soc. 3(52), 1–19 (1986)

    Article  MathSciNet  Google Scholar 

  9. Top J.: Curves of genus 3 over small finite fields. Indag. Math. (N.S.) 14, 275–283 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Herivelto Borges.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borges, H. On multi-Frobenius non-classical plane curves. Arch. Math. 93, 541–553 (2009). https://doi.org/10.1007/s00013-009-0056-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-009-0056-x

Mathematics Subject Classification (2000)

Keywords

Navigation