Skip to main content
SpringerLink
Log in

On Elliptic Convolutional Goppa Codes

  • Conference paper
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5527))

Abstract

The algebraic geometric tools used by Goppa to construct block codes with good properties have been also used successfully in the setting of convolutional codes. We present here this construction carried out over elliptic curves, yielding a variety of codes which are optimal with respect to different bounds. We provide a number of examples for different values of their parameters, including some explicit strongly MDS convolutional codes. We also introduce some conditions for certain codes of this class to be MDS.

Research partially supported by the research contract MTM2006-076B of DGI and by Junta de Castilla y León under research project SA029A08.

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

Access this chapter

Log in via an institution
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. Iglesias Curto, J.I.: A study on convolutional codes. Classfication, new families and decoding, Ph.D. thesis, Universidad de Salamanca (2008)

    Google Scholar 

  2. Forney, G.D.: Convolutional codes I: Algebraic structure. IEEE Trans. Information Theory (1970)

    Google Scholar 

  3. Gluesing-Luerssen, H., Rosenthal, J., Smarandache, R.: Strongly MDS convolutional codes. IEEE Trans. Information Theory (52), 584–598 (2006)

    Google Scholar 

  4. Gluesing-Luerssen, H., Schmale, W.: Distance bounds for convolutional codes and some optimal codes (2003), arXiv:math/0305135v1

    Google Scholar 

  5. Goppa, V.D.: Codes associated with divisors. Probl. Peredachi Inform. 13(1), 33–39 (1977); Translation: Probl. Inform. Transmission 13, 22–26 (1977)

    MathSciNet  MATH  Google Scholar 

  6. Goppa, V.D.: Codes on algebraic curves. Dokl. Adad. Nauk SSSR 259, 1289–1290 (1981); Translation: Soviet Math. Dokl. 24, 170–172 (1981)

    MathSciNet  MATH  Google Scholar 

  7. Hartshorne, R.: Algebraic geometry. Grad. Texts in Math., vol. 52. Springer, New York (1977)

    MATH  Google Scholar 

  8. Husemoller, D.: Elliptic curves. Springer, New York (1987)

    Book  MATH  Google Scholar 

  9. Muñoz Porras, J.M., Dominguez Perez, J.A., Iglesias Curto, J.I., Serrano Sotelo, G.: Convolutional Goppa codes. IEEE Trans. Inform. Theory 52(1), 340–344 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Muñoz Porras, J.M., Domínguez Pérez, J.A., Serrano Sotelo, G.: Convolutional codes of Goppa type. AAECC 15, 51–61 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  11. Rosenthal, J., Smarandache, R.: Maximum distance separable convolutional codes. AAECC 10(1), 15 (1999)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1, 37008, Salamanca, Spain

    José Ignacio Iglesias Curto

Authors
  1. José Ignacio Iglesias Curto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avinguda Països Catalans, 26, 43007, Tarragona, Spain

    Maria Bras-Amorós

  2. Department of Mathematics, The Technical University of Denmark, Building 303, 2800, Lyngby, Denmark

    Tom Høholdt

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Iglesias Curto, J.I. (2009). On Elliptic Convolutional Goppa Codes. In: Bras-Amorós, M., Høholdt, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2009. Lecture Notes in Computer Science, vol 5527. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02181-7_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02181-7_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02180-0

  • Online ISBN: 978-3-642-02181-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation