Behavior of Steiner systems of M24

AbstractIn this paper we show that no pair of Steiner systems S(5, 8, 24) can intersect in the octads of certain subspaces of the binary Golay code C, the 12-dimensional vector space over the field of two elements. In fact, we produce different numbers of Steiner systems that intersect in the octads of these subspaces.For every pair of Steiner systems S(5, 8, 24), and S1(5, 8, 24), there exists a permutation γ of $24, the symmetric group of degree 24, that maps the octads of S onto the octads of S1. An interesting method of finding γ is discussed