The generating rank of the space of short vectors in the Leech lattice mod 2

Andries E. Brouwer, Çiçek Güven

Abstract: Consider the partial linear space on the images in Λ/2Λ of the shortest nonzero vectors in the Leech lattice Λ, where the lines are the triples of vectors adding up to zero. We determine the universal embedding dimension and the generating rank of this space (both are 24) and classify its hyperplanes.