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On Elliptic Convolutional Goppa Codes

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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.

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References

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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
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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

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© 2009 Springer-Verlag Berlin Heidelberg

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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

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  • 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)

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