A method for combining algebraic geometric Goppa codes

  • Jens Peter Pedersen
  • Despina Polemi
Algebraic Coding
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1133)


Various methods for combining codes to obtain new ones have been described by MacWilliams and Sloane [10]. In this paper we present another method for combining algebraic geometric (a.g.) Goppa codes to construct new longer codes using function field extensions. We also prove that if one starts with an a.g. code with minimum distance better than expected, then the new code, obtained by this method, will also have minimum distance better than expected. Furthermore, we give an estimate on the improvement of the minimum distance of the new code.

Key words and phrases

algebraic geometric Goppa codes algebraic function fields of one variable elementary abelian extensions 


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  1. 1.
    G.L. Feng and R.R.N. Rao. A novel approach for contruction of algebraic geometric codes from affine plane curves. University of Southwestern Louisiana, preprint, 1992.Google Scholar
  2. 2.
    G.L. Peng and R.R.N. Rao. Decoding of algebraic geometric codes up to designed minimum distance. IEEE Trans. Inf. Theory, 39:37–46, 1993.Google Scholar
  3. 3.
    A. Garcia, S.J. Kim, and R.F. Lax. Goppa codes and Weistrass gaps. Journal of Pure and Applied Algebra, 84:199–207, 1992.Google Scholar
  4. 4.
    A. Garcia and R.F. Lax. Goppa codes and Weistrass gaps. Lecture Notes in Mathematics, Springer Verlag, 1518:33–42, 1992.Google Scholar
  5. 5.
    V.D. Goppa. Codes on algebraic curves. Soviet Math. Doklady, 24:170–172, 1981.Google Scholar
  6. 6.
    V.D. Goppa. Algebraic geometric codes. Mathematics of the USSR Izvestiya, 21, no.1:75–91, 1983.Google Scholar
  7. 7.
    V.D. Goppa. Codes and information. Russian Mathematical Surveys, 39, no.1:87–141, 1984.Google Scholar
  8. 8.
    V.D. Goppa. Geometry and Codes. Kluwer Academic Publishers, The Netherlands, 1988.Google Scholar
  9. 9.
    C. Kirfel and R. Pellikaan. The minimum distance of codes in an array comming from telescopic semigroups. Eindhoven University of Technology, 1993. preprint.Google Scholar
  10. 10.
    F.J. MacWilliams and N.J.A Sloane. The Theory of Error Correcting Codes. North Holland, New York, 1977.Google Scholar
  11. 11.
    H Stichtenoth. Algebraic Function Fields and Codes. Springer-Verlag, New York, 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jens Peter Pedersen
    • 1
  • Despina Polemi
    • 2
  1. 1.Department of Mathematics and Computer ScienceAalborg UniversityDenmark
  2. 2.Department of MathematicsState University of New YorkFarmingdale

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