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Singular algebraic curves over finite fields

  • Coding and Cryptography
  • Conference paper
  • First Online:
Information Theory and Applications (ITA 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 793))

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Abstract

This paper presents algorithms for the identification and resolution of rational and non-rational singularities (by means of blowings-up) of a projective plane curve C: F(x 1, x 2, x 3)=0 with coefficients in a finite field k. As a result, the genus of the curve is computed. In addition the running time of the algorithms are also analyzed.

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References

  1. S. Abhyankar and C. Bajaj. Computations with algebraic curves. Lecture Notes in Computer Science, Springer-Verlag, 358, July 1988.

    Google Scholar 

  2. M. Bronstein, M. Hassner, A. Vasquez, and C.J. Williamson. Computer algebra algorithms for the construction of error correcting codes on algebraic curves. IEEE Proceedings on Information Theory, June 1991.

    Google Scholar 

  3. D. Le Brigand and J.J. Risler. Algorithm de Brill-Noether et codes de Goppa. Bull. Soc. math. France, 116:231–253, 1988.

    Google Scholar 

  4. D. Polemi. The Brill-Noether Theorem for Finite Fields and an Algorithm for Finding Algebraic Geometric Goppa Codes. Proceedings of the IEEE International Symposium on Information Theory, p.38, Budapest, Hungary, 1991.

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  5. D. Polemi, C. Moreno, and O. Moreno. A construction of a.g. Goppa codes from singular curves. submitted for publication, 1992.

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  6. T. Sakkalis. The topological configuration of a real algebraic curve. Bull. Austr. Math. Soc., 43:37–50, 1991.

    Google Scholar 

  7. T. Sakkalis and R. Farouki. Singular points of algebraic curves. Journal of Symbolic Computation, 9:405–421, 1990.

    Google Scholar 

  8. S. Vladut and Y. Manin. Linear codes and modular curves. Journal of Soviet Mathematics, 30, no. 6:2611–2643, 1985.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, State University of New York, 11735, Farmingdale, NY

    Despina Polemi

  2. Department of Mathematical Sciences, Oakland University, 48309, Rochester, MI

    Takis Sakkalis

Authors
  1. Despina Polemi
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  2. Takis Sakkalis
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Editor information

T. Aaron Gulliver Norman P. Secord

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© 1994 Springer-Verlag Berlin Heidelberg

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Polemi, D., Sakkalis, T. (1994). Singular algebraic curves over finite fields. In: Gulliver, T.A., Secord, N.P. (eds) Information Theory and Applications. ITA 1993. Lecture Notes in Computer Science, vol 793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57936-2_28

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  • DOI: https://doi.org/10.1007/3-540-57936-2_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-57936-6

  • Online ISBN: 978-3-540-48392-2

  • eBook Packages: Springer Book Archive

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