Designs, Codes and Cryptography

, Volume 21, Issue 1, pp 149–164

Equilateral Dimension of the Rectilinear Space

  • Jack Koolen
  • Monique Laurent
  • Alexander Schrijver
Article

DOI: 10.1023/A:1008391712305

Cite this article as:
Koolen, J., Laurent, M. & Schrijver, A. Designs, Codes and Cryptography (2000) 21: 149. doi:10.1023/A:1008391712305

Abstract

Itis conjectured that there exist at most 2k equidistantpoints in the k-dimensional rectilinear space.This conjecture has been verified for k ≤ 3; we show here its validity in dimension k = 4. We alsodiscuss a number of related questions. For instance, what isthe maximum number of equidistant points lying in the hyperplane:\(\sum\nolimits_{i = 1}^k {x_i } = 0?\) If this number would be equal to k, then the above conjecture would follow. Weshow, however, that this number is ≥ k + 1 for k ≥ 4.

Touching number rectilinear space equidistant set cut metric design touching simplices 

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Jack Koolen
    • 1
  • Monique Laurent
    • 1
  • Alexander Schrijver
    • 1
  1. 1.CWISJ AmsterdamThe Netherlands

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