Abstract
The p-rank of a Steiner quadruple system B is the dimension of the linear span of the set of characteristic vectors of blocks of B over GF(p). We derive a formula for the number of different Steiner quadruple systems of order v and given 2-rank r, r<v. Our result extends previous work on enumerating Steiner quadruple systems according to the rank of their codes over GF(2), mainly by V.A. Zinoviev and D.V. Zinoviev.
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