Abstract
We consider sets of (0, +1)-vectors in R n, having exactly s non-zero positions. In some cases we give best or nearly best possible bounds for the maximal number of such vectors if all the pairwise scalar products belong to a fixed set D of integers. The investigated cases include D={ -d, d}, which corresponds to equiangular lines.
Similar content being viewed by others
References
Bland, R. and Las Vergnas, M.: ‘Orientability of matroids’. J. Comb. Theory B 24 (1978), 94–123.
Bos, A. and Seidel, J. J.: ‘Unit Vectors with Non-Negative Inner Products’. Technological University Eindhoven, Memorandum 1980, 10.
Delsarte, P., Goethals, J. M. and Seidel, J. J.: ‘Spherical Codes and Designs’. Geom. Dedicata 6 (1977), 363–388.
Deza, M. Erdös, P. and Frankl, P.: ‘Intersection Properties of Systems of Finite Sets’. Proc. London Mat Soc. 36 (1978), 369–384.
Deza, M. and Frankl, P.: ‘Every Large Set of Equidistant (0, +1, -1)-Vectors Forms a Sunflower’. Combinatorica 1 (1981), 225–231.
Dey, A. and Midha, C. K.: ‘Generalized Balanced Matrices and their Applications’. Utilitas Math. 10 (1976), 139–149.
Dunkl, C. F.: ‘A Krawtchouk Polynomial Addition Theorem and Wreath Product of Symmetric Groups’. Indiana Univ. Math. J. 25–4 (1976), 335–358.
Eades, P.: ‘Circulant (v, k, μ) Designs’. Proc. 7th Australian Conf. on Combinatorial Math., Newcastle, 1979; Lecture Notes in Math., 829, Springer, Berlin (1980), pp. 83–93.
Lemmens, P. W. H. and Seidel, J. J.: ‘Equiangular Lines’. J. Algebra 24 (1973), 494–512.
Levenstein, V. I.: ‘On the Maximum Cardinality of Codes with Bounded Absolute Value for Scalar Products’. Dokl. Akad. Nauk 263 (1982), 1303–1308 (in Russian).
Neumaier, A.: ‘Combinatorial Configurations in Therms of Distances’. Technological University Eindhoven, Memorandum 1981, 09.
Ramsey, F. P.: ‘On a Problem of Formal Logic’. Proc. London Math. Soc. 30 (1930), 264–286.
Tarnanen, H. K.: ‘On the Nonbinary Johnson Scheme’. Abstract of papers, Int. Symp. on Information Theory, 1982, Les Arcs, France, pp. 55–56.
Street, D. Y. and Rodger, C. A.: ‘Some results on Bhascar Rao designs’, Lecture Notes in Math., 829, Springer, Berlin (1980), pp. 238–245.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Deza, M., Frankl, P. On t-distance sets of (0, ±1)-vectors. Geom Dedicata 14, 293–301 (1983). https://doi.org/10.1007/BF00146909
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00146909