Every large set of equidistant (0, +1, −1)-vectors forms a sunflower

Abstract

A theorem of Deza asserts that ifH 1, ...,H m ares-sets any pair of which intersects in exactlyd elements and ifms 2s+2, then theH i form aΔ-system, i.e.\(\left| {\bigcap\limits_{i = 1}^m {H_i } } \right| = d\). In other words, every large equidistant (0, 1)-code of constant weight is trivial. We give a (0, +1, −1) analogue of this theorem.

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Deza, M., Frankl, P. Every large set of equidistant (0, +1, −1)-vectors forms a sunflower. Combinatorica 1, 225–231 (1981). https://doi.org/10.1007/BF02579328

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AMS subject classification (1980)

  • 05 C 65
  • 05 C 35, 05 B 25