Skip to main content
Log in

On t-distance sets of (0, ±1)-vectors

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bland, R. and Las Vergnas, M.: ‘Orientability of matroids’. J. Comb. Theory B 24 (1978), 94–123.

    Google Scholar 

  2. Bos, A. and Seidel, J. J.: ‘Unit Vectors with Non-Negative Inner Products’. Technological University Eindhoven, Memorandum 1980, 10.

  3. Delsarte, P., Goethals, J. M. and Seidel, J. J.: ‘Spherical Codes and Designs’. Geom. Dedicata 6 (1977), 363–388.

    Google Scholar 

  4. Deza, M. Erdös, P. and Frankl, P.: ‘Intersection Properties of Systems of Finite Sets’. Proc. London Mat Soc. 36 (1978), 369–384.

    Google Scholar 

  5. Deza, M. and Frankl, P.: ‘Every Large Set of Equidistant (0, +1, -1)-Vectors Forms a Sunflower’. Combinatorica 1 (1981), 225–231.

    Google Scholar 

  6. Dey, A. and Midha, C. K.: ‘Generalized Balanced Matrices and their Applications’. Utilitas Math. 10 (1976), 139–149.

    Google Scholar 

  7. Dunkl, C. F.: ‘A Krawtchouk Polynomial Addition Theorem and Wreath Product of Symmetric Groups’. Indiana Univ. Math. J. 25–4 (1976), 335–358.

    Google Scholar 

  8. 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.

    Google Scholar 

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

    Google Scholar 

  10. 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).

    Google Scholar 

  11. Neumaier, A.: ‘Combinatorial Configurations in Therms of Distances’. Technological University Eindhoven, Memorandum 1981, 09.

  12. Ramsey, F. P.: ‘On a Problem of Formal Logic’. Proc. London Math. Soc. 30 (1930), 264–286.

    Google Scholar 

  13. Tarnanen, H. K.: ‘On the Nonbinary Johnson Scheme’. Abstract of papers, Int. Symp. on Information Theory, 1982, Les Arcs, France, pp. 55–56.

    Google Scholar 

  14. Street, D. Y. and Rodger, C. A.: ‘Some results on Bhascar Rao designs’, Lecture Notes in Math., 829, Springer, Berlin (1980), pp. 238–245.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00146909

Keywords

Navigation