Skip to main content

Hunting for Curves with Many Points

  • Conference paper
Coding and Cryptology (IWCC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5557))

Included in the following conference series:

Abstract

We construct curves with many points over finite fields by using the class group.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Howe, E., Lauter, K.: Improved upper bounds for the number of points on curves over finite fields. Ann. Inst. Fourier 53, 1677–1737 (2003); corrigendum to: Improved upper bounds for the number of points on curves over finite fields. Ann. Inst. Fourier (Grenoble) 57(3), 1019–1021 (2007)

    Google Scholar 

  2. Niederreiter, H., Xing, C.P.: Explicit global function fields over the binary field with many rational places. Acta Arithm. 75, 383–396 (1996)

    MathSciNet  MATH  Google Scholar 

  3. Niederreiter, H., Xing, C.P.: Cyclotomic function fields, Hilbert class fields and global function fields with many rational places. Acta Arithm. 79, 59–76 (1997)

    MathSciNet  MATH  Google Scholar 

  4. Niederreiter, H., Xing, C.P.: Global function fields fields with many rational points over the ternary field. Acta Arithm. 83, 65–86 (1998)

    MATH  Google Scholar 

  5. Niederreiter, H., Xing, C.P.: Algebraic curves with many rational points over finite fields of characteristic 2. In: Proc. Number Theory Conference (Zakopane 1997), pp. 359–380. de Gruyter, Berlin (1999)

    Google Scholar 

  6. Niederreiter, H., Xing, C.P.: Rational Points on Curves over Finite Fields—Theory and Applications. London Math. Soc. Lecture Note Ser., vol. 285. Cambridge University Press, Cambridge (2002)

    MATH  Google Scholar 

  7. Serre, J.-P.: Letter to G. van der Geer, September 1 (1997)

    Google Scholar 

  8. Serre, J.-P.: Rational points on curves over finite fields. Notes of lectures at Harvard University (1985)

    Google Scholar 

  9. Stichtenoth, H.: Algebraic Function Fields and Codes. Universitext. Springer, Heidelberg (1993)

    MATH  Google Scholar 

  10. van der Geer, G., van der Vlugt, M.: Tables of curves with many points. Math. Comp. 69(230), 797–810 (2000), http://www.science.uva.nl/~geer/tables-mathcomp20.pdf

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

van der Geer, G. (2009). Hunting for Curves with Many Points. In: Chee, Y.M., Li, C., Ling, S., Wang, H., Xing, C. (eds) Coding and Cryptology. IWCC 2009. Lecture Notes in Computer Science, vol 5557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01877-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-01877-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01813-8

  • Online ISBN: 978-3-642-01877-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics