A group-theoretic framework for the construction of packings in grassmannian spaces

By using totally isotropic subspaces in an orthogonal space Omega(+)(2i, 2), several infinite families of packings of 2(k) -dimensional subspaces of real 2(i) -dimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with Barnes-Wall lattices, Kerdock sets and quantum-error-correcting codes.