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Evaluation codes at singular points of algebraic differential equations

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Abstract

We use the special geometry of singular points of algebraic differential equations on the affine plane over finite fields to study the main features and parameters of error correcting codes giving by evaluating functions at sets of singular points. In particular, one gets new methods to construct codes with designed minimum distance.

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Authors and Affiliations

  1. Departamento de Algebra, Geometria y Topologia, Universidad de Valladolid, Valladolid, Spain

    A. Campillo

  2. Departamento de Matematica Aplicada, University of Valladolid, Valladolid, Spain

    J. I. Farran

  3. Departamento de Matematicas, Universidad de León, León, Spain

    M. J. Pisabarro

Authors
  1. A. Campillo
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  2. J. I. Farran
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  3. M. J. Pisabarro
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Corresponding author

Correspondence to A. Campillo.

Additional information

This work was partially supported by MCyT BFM2001-2251.

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Campillo, A., Farran, J.I. & Pisabarro, M.J. Evaluation codes at singular points of algebraic differential equations. AAECC 18, 191–203 (2007). https://doi.org/10.1007/s00200-006-0024-7

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  • DOI: https://doi.org/10.1007/s00200-006-0024-7

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