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Zeta Functions of Some Curves and Minimal Exponent for Pellikaan’s Decoding Algorithm of Algebraic-Geometric Codes

  • Ph. Carbonne
  • A. Thiong Ly
Part of the International Centre for Mechanical Sciences book series (CISM, volume 339)

Abstract

It is shown that the Pellikaan’s decoding algorithm of some families of Goppa codes CΩ(D, G) needs at most (g+1) effective divisors if the degree of G is odd and at most ⌊lg/2⌋+1 effective divisors if the degree is even, where g is the genus of the curve used.

Keywords

Zeta Function Finite Field Decode Algorithm Maximal Curve Effective Divisor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    P. Carbonne. Calcul de quelques fonctions Zeta. Preprint.Google Scholar
  2. [2]
    C.J. Moreno. Algebraic curves over finite fields. Cambridge Tracts in Mathematics 97, Cambridge University Press 1991.Google Scholar
  3. [3]
    R. Pellikaan. on a decoding algorithm for codes on maximal curves. IEEE Trans Info Theory Vol 35, 6 (1989), 1228–1232.CrossRefMATHMathSciNetGoogle Scholar
  4. [4]
    ]S.G. Vladuts. On the decoding of Algebraic Geometric Codes over Fq for q≥16. IEEE Trans Info Theory Vol 36, 6 (Nov 1990), 1461–1463.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • Ph. Carbonne
    • 1
  • A. Thiong Ly
    • 1
  1. 1.University of Toulouse le MirailToulouseFrance

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