A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
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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