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Evaluation codes at singular points of algebraic differential equations

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

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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References

  1. Campillo A. and Olivares J. (2000). Assigned conditions and geometry of foliations on the projective plane. Advanced Studies in Pure Mathematics. Math. Soc. Japan 29: 97–113

    MathSciNet  Google Scholar 

  2. Campillo A. and Olivares J. (2001). Polarity with respect to a foliation and Cayley–Bacharach theorems. J. Reine Angew Math. 534: 95–118

    MathSciNet  Google Scholar 

  3. Campillo A. and Olivares J. (2003). On sections with isolated singularities of twisted bundles and applications to foliations by curves. Math. Res. Lett. 10(5–6): 651–658

    MathSciNet  Google Scholar 

  4. Eisenbud D., Green M. and Harris J. (1996). Cayley–Bacharach theorems and conjectures. Bull. Amer. Math. Soc. 33(3): 295–324

    Article  MathSciNet  Google Scholar 

  5. Greuel, G.-M., Pfister, G., Schönemann, H.: SINGULAR 2.0: A computer algebra system for polynomial computations. Centre for Computer Algebra, University of Kaiserslautern (2001). Available via http://www.singular.uni-kl.de/

  6. Hansen J. (2003). Linkage and codes on complete intersections. Applicable Algebra in Engineering. Communication and Computing 14(3): 175–185

    MathSciNet  Google Scholar 

  7. Hoholdt, T., Van Lint, J.H., Pellikaan, R.: Algebraic geometric of codes. In: Handbook of coding theory, vol. I, pp. 871–961. Elsevier, North-Holland, Amsterdam (1998)

  8. MacWilliams, F.J., Sloane, N.: The theory of error-correcting codes. In: North Holland Mathematical Library, vol. 16. North Holland Publication Co., Amsterdam (1977)

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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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