Skip to main content

Spherical codes and designs

This is a preview of subscription content, access via your institution.

References

  1. Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, Dover, New York, 1965.

    Google Scholar 

  2. Askey, R., ‘Orthogonal Polynomials and Special Functions’, Regional Conference Lectures in Applied Mathematics, SIAM 21 (1975).

  3. Assmus, E.F. and Mattson, H.F., ‘New 5-Designs’, J. Combin. Theory 6, 122–151 (1969).

    MATH  Article  MathSciNet  Google Scholar 

  4. Bose, R. C. and Mesner, D. M., ‘On Linear Associative Algebras Corresponding to Association Schemes of Partially Balanced Designs’, Ann. Math. Statist. 30, 21–38 (1959).

    MATH  Article  MathSciNet  Google Scholar 

  5. Cameron, P.J. and Lint, J.H van, ‘Graph Theory, Coding Theory and Block Designs’, London Math. Soc. Lecture Note, Ser. 19, Cambr. Univ. Press, 1975.

  6. Coxeter, H.S.M., Regular Polytopes, 3rd Edn, Dover, 1973.

  7. Delsarte, P., ‘An Algebraic Approach to the Association Schemes of Coding Theory’, Philips Res. Repts. Suppl., No. 10 (1973).

  8. Delsarte, P., ‘Four Fundamental Parameters of a Code and their Combinatorial Significance’, Inform. Control 23, 407–438 (1973).

    MATH  Article  MathSciNet  Google Scholar 

  9. Delsarte, P., ‘Hahn Polynomials Discrete Harmonics, and t-Designs’, SIAM J. Appl. Math. (to appear).

  10. Delsarte, P. and Goethals, J.M., ‘Unrestricted Codes with the Golay Parameters are Unique’, Discrete Math. 12, 212–224 (1975).

    Article  MathSciNet  Google Scholar 

  11. Delsarte, P., Goethals, J. M. and Seidel, J.J., ‘Bounds for Systems of Lines, and Jacobi Polynomials’, Philips Res. Repts. 30, 91*-105* (1975). Bouwkamp volume.

    MATH  Google Scholar 

  12. Hadwiger, H., ‘Über ausgezeichnete Vektorsterne und reguUire Polytope’, Comm. Math. Helv. 13, 90-l07 (1940).

    Article  MathSciNet  Google Scholar 

  13. Higman, D. G., ‘Coherent Configurations, Part I, Ordinary Representation Theory’, Geometriae Dedicata 4, 1–32 (1975).

    MATH  Article  MathSciNet  Google Scholar 

  14. Hughes, D.R., ‘On t-Designs and Groups’, Am. J. Math. 87, 761–778 (1965).

    MATH  Article  Google Scholar 

  15. Koornwinder, T.H., ‘The Addition Formula for Jacobi Polynomials and Spherical Harmonics’, SIAM J. Appl. Math. 2, 236–246 (1973).

    Article  MathSciNet  Google Scholar 

  16. Koornwinder, T.H., ‘A Note on the Absolute Bound for Systems of Lines’, Proc. Kon. Nederl. Akad. Wet. Ser. A 79 (Indag. Math. 38), 152–153 (1976).

    MATH  MathSciNet  Google Scholar 

  17. Lemmens, P. W. H. and Seidel, J.J., ‘Equiangular Lines’ J. Alg. 24, 494–512 (1973).

    MATH  Article  MathSciNet  Google Scholar 

  18. Lint, J.H van, ‘On the Nonexistence of Perfect 2- and 3-Hamming-Error-Correcting Codes over GF(q)’, Inform. Control 16, 396–401 (1970).

    MATH  Article  Google Scholar 

  19. Lint, J.H. van, and Seidel, J.J., ‘Equilateral Point Sets in Elliptic Geometry’, Proc. Kon. Nederl. Akad. Wet. Ser. A 69 (Indag. Math. 28), 335–348 (1966).

    Google Scholar 

  20. McKay, J., ‘A Setting for the Leech Lattice’, p. 117 in Finite Groups 72 (eds. T. Hagen, M. P. Hale, E. E. Shult), North-Holland, 1973, and private communication.

  21. Rankin, R.A., ‘The Closest Packing of Spherical Caps in n Dimensions’, Proc. Glasgow Math. Assoc. 2, 139–144 (1955).

    MATH  Article  MathSciNet  Google Scholar 

  22. Scott, L. L., ‘A Condition on Higman‘s Parameters’, AMS Notices, Jan. 1973, 701-20-45.

  23. Scott, L.L., ‘Some Properties of Character Products’, J. Alg. 45, 259–265 (1977).

    MATH  Article  Google Scholar 

  24. Seidel, J.J., ‘A Survey of Two-graphs’, Proc. Intern. Coll. Teorie Comb., Accad. Naz. Lincei, Roma, 1976, Part I, pp. 481–511.

  25. Seidel, J.J., ‘Graphs and Two-graphs’, 5th Southeastern Conf. on Combinatories, Graph Theory, Computing, Utilitas Math. Publ. Inc., Winnipeg, 1974, pp. 125–143.

    Google Scholar 

  26. Taylor, D.E., ‘Regular Two-graphs’, Proc. London Math. Soc. 35, 257–274 (1977).

    MATH  Article  MathSciNet  Google Scholar 

  27. Wilson, R.M. and Ray-Chaudhuri, D.K., ‘Generalization of Fisher’s Inequality to t-Designs’, AMS Notices 18, 805 (1971).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Delsarte, P., Goethals, J.M. & Seidel, J.J. Spherical codes and designs. Geom Dedicata 6, 363–388 (1977). https://doi.org/10.1007/BF03187604

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03187604

Keywords

  • Regular Graph
  • Association Scheme
  • Harmonic Polynomial
  • Addition Formula
  • Golay Code