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 ifm ≧s ² −s+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.