Order functions and evaluation codes

  • Tom Høholdt
  • Jacobus H. van Lint
  • Ruud Pellikaan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1255)


Based on the notion of an order function we construct and determine the parameters of a class of error-correcting evaluation codes. This class includes the one-point algebraic geometry codes as well as the generalized Reed-Muller codes, and the parameters are determined without using heavy machinery from algebraic geometry.


Weight Function Nonzero Element Evaluation Code Lexicographic Order Order Function 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    V.D. Goppa, “Codes associated with divisors,” Probl. Peredachi Inform. vol. 13 (1), pp. 33–39, 1977. Translation: Probl. Inform. Transmission, vol. 13, pp. 22–26, 1977.Google Scholar
  2. 2.
    M.A. Tsfasman, S.G. Vlăduţ and T. Zink, “Modular curves, Shimura curves and Goppa codes, better than Varshamov-Gilbert bound,” Math. Nachrichten, vol. 109, pp. 21–28, 1982.Google Scholar
  3. 3.
    J. Justesen, K.J. Larsen, H. Elbrønd Jensen, A. Havemose and T. Høholdt, “Construction and decoding of a class of algebraic geometric codes,” IEEE Trans. Inform. Theory, vol. IT-35, pp. 811–821, July 1989.Google Scholar
  4. 4.
    G.-L. Feng and T.R.N. Rao, “Decoding of algebraic geometric codes up to the designed minimum distance,” IEEE Trans. Inform. Theory, vol. IT-39, pp. 37–45, Jan. 1993.Google Scholar
  5. 5.
    G.-L. Feng and T.R.N. Rao, “A simple approach for construction of algebraic-geometric codes from affine plane curves,” IEEE Trans. Inform. Theory, vol. IT-40, pp. 1003–1012, July 1994.Google Scholar
  6. 6.
    G.-L. Feng, V. Wei, T.R.N. Rao and K.K. Tzeng, “Simplified understanding and efficient decoding of a class of algebraic-geometric codes,” IEEE Trans. Inform. Theory, vol. IT-40, pp. 981–1002, July 1994.Google Scholar
  7. 7.
    G.-L. Feng and T.R.N. Rao, “Improved geometric Goppa codes,” Part I: Basic Theory, IEEE Trans. Inform. Theory, pp. 1678–1693, Nov. 1995.Google Scholar
  8. 8.
    R. Pellikaan, “On the existence of order functions,” Proceedings of the 2nd Shanghai conference on designs, codes and finite geometries, to appear 1997.Google Scholar
  9. 9.
    R.A. Brualdi, W.C. Huffmann and V.S. Pless eds.: Handbook on Coding Theory, Elsevier Amsterdam, to appear.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Tom Høholdt
    • 1
  • Jacobus H. van Lint
    • 1
  • Ruud Pellikaan
    • 2
  1. 1.Dept. of MathematicsTechnical University of DenmarkLyngbyDenmark
  2. 2.Dept. of Mathematics and Computing ScienceEindhoven University of TechnologyMB EindhovenThe Netherlands

Personalised recommendations