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Spherical codes and designs. (English) Zbl 0376.05015


MSC:

05B25 Combinatorial aspects of finite geometries
05B30 Other designs, configurations
51F99 Metric geometry
Full Text: DOI

References:

[1] Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, Dover, New York, 1965. · Zbl 0171.38503
[2] Askey, R., ’Orthogonal Polynomials and Special Functions’, Regional Conference Lectures in Applied Mathematics, SIAM 21 (1975). · Zbl 0298.33008
[3] Assmus, E.F. and Mattson, H.F., ’New 5-Designs’, J. Combin. Theory 6, 122–151 (1969). · Zbl 0179.02901 · doi:10.1016/S0021-9800(69)80115-8
[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). · Zbl 0089.15002 · doi:10.1214/aoms/1177706356
[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. · Zbl 0314.94008
[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). · Zbl 1075.05606
[8] Delsarte, P., ’Four Fundamental Parameters of a Code and their Combinatorial Significance’, Inform. Control 23, 407–438 (1973). · Zbl 0274.94010 · doi:10.1016/S0019-9958(73)80007-5
[9] Delsarte, P., ’Hahn Polynomials Discrete Harmonics, and t-Designs’, SIAM J. Appl. Math. (to appear). · Zbl 0429.05031
[10] Delsarte, P. and Goethals, J.M., ’Unrestricted Codes with the Golay Parameters are Unique’, Discrete Math. 12, 212–224 (1975). · Zbl 0307.94013 · doi:10.1016/0012-365X(75)90047-3
[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. · Zbl 0322.05023
[12] Hadwiger, H., ’Über ausgezeichnete Vektorsterne und reguUire Polytope’, Comm. Math. Helv. 13, 90-l07 (1940). · Zbl 0024.06804 · doi:10.1007/BF01378055
[13] Higman, D. G., ’Coherent Configurations, Part I, Ordinary Representation Theory’, Geometriae Dedicata 4, 1–32 (1975). · Zbl 0333.05010 · doi:10.1007/BF00147398
[14] Hughes, D.R., ’On t-Designs and Groups’, Am. J. Math. 87, 761–778 (1965). · Zbl 0134.03004 · doi:10.2307/2373244
[15] Koornwinder, T.H., ’The Addition Formula for Jacobi Polynomials and Spherical Harmonics’, SIAM J. Appl. Math. 2, 236–246 (1973). · Zbl 0276.33023 · doi:10.1137/0125027
[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). · Zbl 0328.05020
[17] Lemmens, P. W. H. and Seidel, J.J., ’Equiangular Lines’ J. Alg. 24, 494–512 (1973). · Zbl 0255.50005 · doi:10.1016/0021-8693(73)90123-3
[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). · Zbl 0205.47102 · doi:10.1016/S0019-9958(70)90213-5
[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). · Zbl 0138.41702
[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. · Zbl 0257.20005
[21] Rankin, R.A., ’The Closest Packing of Spherical Caps in n Dimensions’, Proc. Glasgow Math. Assoc. 2, 139–144 (1955). · Zbl 0065.15601 · doi:10.1017/S2040618500033219
[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). · Zbl 0363.20006 · doi:10.1016/0021-8693(77)90325-8
[24] Seidel, J.J., ’A Survey of Two-graphs’, Proc. Intern. Coll. Teorie Comb., Accad. Naz. Lincei, Roma, 1976, Part I, pp. 481–511. · Zbl 0352.05016
[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.
[26] Taylor, D.E., ’Regular Two-graphs’, Proc. London Math. Soc. 35, 257–274 (1977). · Zbl 0362.05065 · doi:10.1112/plms/s3-35.2.257
[27] Wilson, R.M. and Ray-Chaudhuri, D.K., ’Generalization of Fisher’s Inequality to t-Designs’, AMS Notices 18, 805 (1971).
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