Designs as maximum codes in polynomial metric spaces
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Bannai E., Ito T., Algebraic Combinatorics. I. Association Schemes, Benjamin/Cummings, London, 1984.
Bose R. C., Strongly regular graphs, partial geometries, and partially balanced designs, Pacific J. Math. 13 (1963) 389?419.
Brouwer A. E., van Lint J. H., Strongly regular graphs and partial geometries, In: Enumeration and Design, Academic Press, Toronto, 1984, pp. 85?122.
Calderbank R., On uniformly packed [n,n?k,4] codes over GF(q) and a class of caps in PG(k?1,q), J. London Math. Soc. 26 (1982), 365?384.
Calderbank R., Kantor W.M., The geometry of two-weight codes, Bull. London Math. Soc. 18 (1986), 97?122.
Cameron P. J., Goethals J.-M., Seidel J. J., Strongly regular graphs having strongly regular subconstituents, J. Algebra 43 (1978), 257?280.
Delsarte Ph., An algebraic approach to the association schemes of coding theory, Philips Res. Reports, Suppl. 10 (1973).
Delsarte Ph., Goethals J.-M., Seidel J. J., Bounds for systems of lines, and Jacobi polynomials, Philips Res. Reports 30 (1975), 91?105.
Delsarte Ph., Goethals J.-M., Alternating bilinear forms over GF(q), J. Combin. Th. (A) 19 (1975), 26?50.
Delsarte Ph., Associations schemes and t-design in regular semilattices, J. Combin. Th. (A) 20 (1976), 230?243.
Delsarte Ph., Goethals J.-M., Seidel J. J., Spherical codes and designs, Geometriae Dedicata 6 (1977), 363?388.
Delsarte Ph., Hahn polynomials, discrete harmonics, and t-designs, SIAM J. Appl. Math. 34 (1978), 157?166.
Delsarte Ph., Bilinear forms over a finite field with application to coding theory J. Combin. Th. (A) 25 (1978), 226?241.
Denniston R. H. F., Some maximal arcs in finite projective planes. I, Combin. Th. 6 (1969), 317?319.
Fazekas G., Levenshtein V. I., On upper bounds for code distance and covering radius of designs in polynomial metric spaces In: Fifth Joint Soviet-Swedish Intern. Workshop Inform. Theory, Moscow, 1990, pp. 65?68.
Gabidulin E. M., Theory of codes with maximal rank distance, Problems of Information Transmission 21 (1985).
Gasper G., Linearization of the product of Jacobi polynomials. I, Canad. J. Math. 22: (1) (1970), 171?175.
Gelfand I. M., Spherical functions on symmetric Riemannian spaces, Amer. Math. Soc. Transl. 37: (2) (1964), 39?43.
Helgason S., Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
Hill R., On the largest size cap in S 5,3Rend. Accad. Naz. Lincei 54: (8) (1973), 378?384.
Hill R., Caps and groups, In: Atti dei Covegni Lincei, Colloquio Intern. sulle Theorie Combinatorie (Roma, 1973), No. 17 (Accad. Naz. Licei), 1976, 384?394.
Hoggar S. G., Bounds for quaternionic line systems and reflection groups, Math. Scand. 43 (1978), 241?249.
Kabatiansky G. A., Levenshtein V. I., Bounds for packings on a sphere and in space, Problems of Information Transmission 14: (1) (1978), 1?17.
Koornwinder T., The addition formula for Jacobi polynomials and spherical harmonics, SIAM J. Appl. Math. 25 (1973), 236?246.
Krein M. G., Nudelman A. A., Problems of Markov's Moments and Extremal Problems, Nauka, Moscow, 1973 (in Russian).
Leonard D. A., Orthogonal polynomials, duality and association schemes, SIAM J. Math. 13 (1982), 656?663.
Levenshtein V. I., On choosing polynomials to obtain bounds in packing problems, In: Proc. Seventh All-Union Conf. on Coding Theory and Information Transmission, Part II, Moscow, Vilnius, 1978, pp. 103?108 (in Russian).
Levenshtein V. I., On bounds for packings in n-dimensional Euclidean space, Soviet Math. Dokl. 20: (2) (1979), 417?421.
Levenshtein V. I., Bounds on the maximal cardinality of a code with bounded modulus of the inner product, Soviet Math. Dokl. 25: (2) (1982), 526?531.
Levenshtein V.I., Bounds for packings of metric spaces and some their applications In: Probl. Cybern. 40, Nauka, Moscow, 1983, pp. 43?110 (in Russian).
Levenshtein V. I., Packing of polynomial metric spaces, In: Proc. Third International Workshop on Information Theory, Sochi, 1987, pp. 271?274.
MacWilliams F. J., Sloane N. J. A., The Theory of Error-Correcting Codes, North Holland, Amsterdam, 1977.
McEliece R. J., Rodemich E. R., Rumsey H., Jr., Welch L.R., New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities, IEEE Trans. Inform. Theory IT-23 (1977), 157?166.
Neumaier A., Combinatorial Configurations in Terms of Distances, Memorandum 81-09 (Wiskunde), Eindhoven Univ. Technol., 1981.
Odlyzko A. M., Sloane N. J. A., New upper bounds on the number of units spheres that can touch a unit sphere in n dimensions, J. Combin. Th. (A) 26 (1979), 210?214.
Semakov N. V., Zinov'ev V. A., Equidistant q-ary codes and resolved balanced imcomplete block designs, Problems of Information Transmission, 4: (2) (1968).
Semakov N. V., Zinov'ev V. A., Zaitsev G. V., Class of maximal equidistant codes, Problems of Information Transmission 5: (2) (1969).
Semakov N. V., Zinov'ev V. A., Equally-weighted codes and tactical configurations, Problems of Information Transmission 5 (3) (1969) 22?28.
Sidelnikov V. M., On extremal polynomials used to estimate the size of codes, Problems of Information Transmission 16: (3) (1980), 174?186.
Sloane N. J. A., Recent bounds for codes, sphere packing and related problems obtained by linear programming and others methods, Contemporary Mathematics 9 (1982), 153?185.
Stanton D., A partially ordered set and q-Krawtchouk polynomials, J. Combin. Th.(A) 30 (1981), 276?284.
Terwilliger P., A characterization of P-and Q-polynomial schemes, J. Combin. Th. (A) 45 (1987), 8?26.
Thas J. A., On 4-gonal configuration with parameters r=q 2 +1 and k=q+1. Part I, Geom. Dedicata 3 (1974), 365?375.
Tietavainen A., Covering radius problems and character sums, In: Proc. Fourth Joint Swedish-Soviet International Workshop on Information Theory, Gotland, Sweden, 1989, pp. 196?198.
Vilenkin N. J., Special Functions and the Theory of Group Representations, Amer. Math. Soc., Providence, RI, 1968.