Dimension of the space generated by Steiner systems.

To every Steiner system with parameters (t,k,v) on {1,...,v} and blocks B, we can assign its characteristic vector χB, which is a (0,1)‐vector whose entries are indexed by the k‐subsets of {1,...,v} such that for each k‐subset A of {1,...,v},χB(A)=1 if and only if A∈B. In this paper, we show that the dimension of the vector space generated by all of the characteristic vectors of Steiner systems with parameters (t,k,v) is (vk)−(vt)+1, provided that 1≤t≤k≤v/2 and there is at least one such system. [ABSTRACT FROM AUTHOR]