Recursive Towers of Function Fields over Finite Fields | SpringerLink
Skip to main content

Recursive Towers of Function Fields over Finite Fields

  • Conference paper
Arithmetic of Finite Fields (WAIFI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6087))

Included in the following conference series:

  • 760 Accesses

Abstract

The theory of recursive towers of function fields over finite fields was developed by A. Garcia and the author since 1995. We give a survey about the main ideas and results, and we propose some problems for future work.

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

Access this chapter

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
JPY 3498
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
JPY 5719
Price includes VAT (Japan)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
JPY 7149
Price includes VAT (Japan)
  • 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.

Similar content being viewed by others

References

  1. Bassa, A., Garcia, A., Stichtenoth, H.: A New Tower over Cubic Finite Fields. Moscow Math. Journal 8(3), 401–418 (2008)

    MATH  MathSciNet  Google Scholar 

  2. Cramer, R.: Private Communication (2010)

    Google Scholar 

  3. Duursma, I., Poonen, B., Zieve, M.: Everywhere ramified towers of global function fields. In: Mullen, G.L., Poli, A., Stichtenoth, H., et al. (eds.) Fq7 2003. LNCS, vol. 2948, pp. 148–153. Springer, Heidelberg (2004)

    Google Scholar 

  4. Garcia, A., Stichtenoth, H.: On the Asymptotic Behaviour of Some Towers of Function Fields over Finite Fields. J. Number Theory 61, 248–273 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  5. Garcia, A., Stichtenoth, H.: On Tame Towers over Finite Fields. J. Reine Angew. Math. 557, 53–80 (2003)

    MATH  MathSciNet  Google Scholar 

  6. Garcia, A., Stichtenoth, H.: Explicit Towers of Function Fields over Finite Fields. In: Topics in Geometry, Coding Theory and Cryptography, pp. 1–58. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Garcia, A., Stichtenoth, H., Thomas, M.: On Towers and Composita of Towers of Function Fields over Finite Fields. Finite Fields and Appl. 3, 257–274 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Goppa, V.D.: Codes on Algebraic Curves. Soviet Math. Dokl. 24(1), 170–172 (1981)

    MATH  Google Scholar 

  9. Hu, X., Maharaj, H.: On the qth Power Algorithm. Finite Fields and Appl. 14, 1068–1082 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Niederreiter, H., Xing, C.P.: Algebraic Geometry in Coding Theory and Cryptography. Princeton University Press, Princeton (2009)

    MATH  Google Scholar 

  11. Serre, J.-P.: Sur le Nombre des Points Rationnels d’une Courbe Algébrique sur un Corps Finis. C. R. Acad. Sci. Paris 296, 397–402 (1983)

    MATH  MathSciNet  Google Scholar 

  12. Stichtenoth, H.: Algebraic Function Fields and Codes, 2nd edn. Graduate Texts in Mathematics, vol. 254. Springer, Heidelberg (2009)

    MATH  Google Scholar 

  13. Tsfasman, M.A., Vladut, S.G., Zink, T.: Modular Curves, Shimura Curves, and Goppa Codes, Better than the Varshamov-Gilbert Bound. Math. Nachr. 109, 21–28 (1982)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Stichtenoth, H. (2010). Recursive Towers of Function Fields over Finite Fields. In: Hasan, M.A., Helleseth, T. (eds) Arithmetic of Finite Fields. WAIFI 2010. Lecture Notes in Computer Science, vol 6087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13797-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13797-6_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13796-9

  • Online ISBN: 978-3-642-13797-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics