Generalized quadratic-residue codes

  • J. H. van Lint
Part of the International Centre for Mechanical Sciences book series (CISM)


At the 1975 CISM Summer School on Information Theory P. Camion (cf. [1]) introduced “global quadratic abelian codes” which are a generalization of (classical) quadratic residue codes (QR-codes). A year earlier H.N. Ward (cf. [8]) had used symplectic geometry to introduce a generalization of QR-codes. Both presentations rely heavily on abstract algebra. Essentially such codes (at least in the binary case) were introduced by Ph. Del-sarte in 1971 (cf. [2]) as codes generated by the adjacency matrices of finite miquelian inversive planes. Recently J.H. van Lint and F.J. Mac-Williams (cf. [4]) showed that the methods that are used to treat QR-codes can easily be generalized to give a completely analogous treatment of the so-called generalized quadratic residue codes (GQR-codes).


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  1. 1.
    Camion, P., Global Quadratic Abelian Codes, in Information Theory, CISM Courses and Lectures 219, G. Longo, ed., Springer-Verlag, Wien 1975.Google Scholar
  2. 2.
    Delsarte, P.-, Majority Logic Decodable Codes Derived from Finite l’nver-sive Planes, Inf. and Control 18, 1971, 319–325.MathSciNetCrossRefGoogle Scholar
  3. 3.
    van Lint J.H., Coding Theory, Lecture Notes in Math. 201, Springer-Verlag, Berlin, 1971.zbMATHGoogle Scholar
  4. 4.
    van Lint J.H. and F.J. MacWilliams, Generalized Quadratic Residue Codes, IEEE Trans, on Information Theory 24 (1978).Google Scholar
  5. 5.
    MacWilliams, F.J. and N.J.A. Sloane, The Theory of Error-Correcting Codes, North-Holland, Amsterdam, 1977.zbMATHGoogle Scholar
  6. 6.
    Sands, A.D., On the Factorization of Finite Abelian Groups, Acta Math. Acad. Sci. Hung. 13, 1962, 153–159.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    van Tilborg, H.C.A., On Weights in Codes, Report 71-WSK-03, Dept. of Mathematics, Technological University Eindhoven, 1971.zbMATHGoogle Scholar
  8. 8.
    Ward, H.N., Quadratic Residue Codes and Symplectic Groups, J. of Algebra 29, 1974, 150–171.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Wien 1979

Authors and Affiliations

  • J. H. van Lint
    • 1
  1. 1.Department of MathematicsEindhoven University of TechnologyThe Netherlands

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