Skip to main content

Decoding Algebraic-Geometric Codes by solving a key equation

  • Conference paper
  • First Online:
Coding Theory and Algebraic Geometry

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1518))

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
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. J.H. van Lint, G. van der Geer, Introduction to Coding Theory and Algebraic Geometry. DMV Seminar, Band 12. Birkhäuser Verlag 1988.

    Google Scholar 

  2. J. Justesen, K.J. Larsen, A. Havemose, H.E. Jensen, T. Høholt, Construction and decoding of a class of algebraic geometry codes. IEEE-IT 35(4)(1989), pp. 811–821.

    Article  MathSciNet  MATH  Google Scholar 

  3. A.N. Skorobogatov, S.G. VlĂduţ, On the decoding of algebraic-geometric codes. IEEE-IT 36(5)(1990),pp. 1051–1060.

    Article  MathSciNet  MATH  Google Scholar 

  4. R. Pellikaan, On a decoding Algorithm for Codes on maximal curves. IEEE-IT 35(6)(1989), pp. 1228–1232.

    Article  MathSciNet  MATH  Google Scholar 

  5. S.G. VlĂduţ, On the decoding of algebraic-geometric codes for q ≥ 16. IEEE-IT 36(6)(1990), pp. 1961–1963.

    MATH  Google Scholar 

  6. S.C. Porter, Decoding Codes arising from Goppa's construction on algebraic curves. Thesis, Yale University, 1988.

    Google Scholar 

  7. S.C. Porter, Decoding Geometric Goppa Codes. Preprint.

    Google Scholar 

  8. S.C. Porter, Euclid's algorithm, resultants and rational function representation on algebraic curves with a single point at infinity. Preprint.

    Google Scholar 

  9. S.C. Porter, Dense representation of affine coordinate rings of curves with one point at infinity. Proceedings of ISSAC-89.

    Google Scholar 

  10. S.C. Porter, An efficient data structure for rational function on algebraic curves. Preprint.

    Google Scholar 

  11. S.C. Porter, B.Z. Shen, R. Pellikaan, Decoding geometric Goppa codes using an extra place. Preprint Eindhoven University, September 1991.

    Google Scholar 

  12. B.Z. Shen, Subresultant sequence on a Weierstrass algebra and its application to decoding algebraic-geometric codes. preprint Eindhoven University, May 1991

    Google Scholar 

  13. D. Ehrhard, Über das Dekodieren Algebraisch-Geometrischer Codes. Thesis, Düsseldorf University, 1991.

    Google Scholar 

Download references

Authors

Editor information

Henning Stichtenoth Michael A. Tsfasman

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag

About this paper

Cite this paper

Ehrhard, D. (1992). Decoding Algebraic-Geometric Codes by solving a key equation. In: Stichtenoth, H., Tsfasman, M.A. (eds) Coding Theory and Algebraic Geometry. Lecture Notes in Mathematics, vol 1518. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087989

Download citation

  • DOI: https://doi.org/10.1007/BFb0087989

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55651-0

  • Online ISBN: 978-3-540-47267-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics