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. 
A.R. Calderbank, R.H. Hardin, E.M. Rains, P.W. Shor, N.J.A. Sloane