Advertisement

Abstract

We present in these lecture notes a survey of Delsarte’s work on the algebraic theory of association schemes, which has influenced considerably the recent developments in coding theory. We have somewhat updated Delsarte’s original results which are often presented with new proofs. The material has been divided into three main parts.

Keywords

Symplectic Form Association Scheme Dual Code Perfect Code Krawtchouk Polynomial 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. [1]
    Cameron, P. J. and van Lint, J. H., Graph Theory, Coding Theory and Block Designs, London Math. Soc. Lecture Note Series, N°19, Cambridge University Press, London, 1975, Chap. 15.zbMATHGoogle Scholar
  2. [2]
    Delsarte, P., “An algebraic approach to the association schemes of coding theory”, Philips Res. Repts. Supplements, N°10, 1973.zbMATHGoogle Scholar
  3. [3]
    Delsarte, P., “The association schemes of coding theory”, in Combinatorics, Mathematical Centre Tracts, n°55, M. Hall, Jr. and J. H. van Lint, Eds., Math. Centrum, Amsterdam, 1974, p. 139.Google Scholar
  4. [4]
    Delsarte, P. and Goethals, J.-M., “Alternating bilinear forms over GF(q)”, J. Combinatorial Theory, Ser. A, vol. 19, pp. 26–50, 1975.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Goethals, J.-M., “Nonlinear codes defined “by quadratic forms over GF(2)”, Information and Control, Vol. 31, pp. 43–74, 1976.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    MacWilliams, F.J. and Sloane, N. J. A., The Theory of Error-Correcting Codes, North-Holland Mathematical Library, Vol. 16, North-Holland, Amsterdam, 1977, Chap. 21.zbMATHGoogle Scholar
  7. [7]
    Sloane, N. J. A., “An introduction to association schemes and coding theory”, in Theory and Applications of Special Functions, R. A. Askey, Ed., Academic Press, New York, 1975, p.225.Google Scholar

Copyright information

© Springer-Verlag Wien 1979

Authors and Affiliations

  • J.-M. Goethals
    • 1
  1. 1.MBLE Research LaboratoryBrusselsBelgium

Personalised recommendations