Equality in the linear algebra bound

Abstract

We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information about the extremal configuration. We obtain results on set families satisfying conditions on pairwise intersections, or Hamming distances. Also, we have an application to 2-distance sets in Euclidean spaces.