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Part of the book series: International Centre for Mechanical Sciences ((CISM))

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.

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Bibliography

  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.

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  2. Delsarte, P., “An algebraic approach to the association schemes of coding theory”, Philips Res. Repts. Supplements, N°10, 1973.

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  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.

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  4. Delsarte, P. and Goethals, J.-M., “Alternating bilinear forms over GF(q)”, J. Combinatorial Theory, Ser. A, vol. 19, pp. 26–50, 1975.

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  5. Goethals, J.-M., “Nonlinear codes defined “by quadratic forms over GF(2)”, Information and Control, Vol. 31, pp. 43–74, 1976.

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  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.

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  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 

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© 1979 Springer-Verlag Wien

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Goethals, JM. (1979). Association Schemes. In: Longo, G. (eds) Algebraic Coding Theory and Applications. International Centre for Mechanical Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-39641-4_5

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  • DOI: https://doi.org/10.1007/978-3-662-39641-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-38752-8

  • Online ISBN: 978-3-662-39641-4

  • eBook Packages: Springer Book Archive

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