A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor, N. J. A. Sloane
Abstract
By using totally isotropic subspaces in an orthogonal space Omega+(2i,2), several infinite families of packings of 2k-dimensional subspaces of real 2i-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.
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