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

Abstract

By using totally isotropic subspaces in an orthogonal space Ω+ (2i, 2), several infinite families of packings of 2^k-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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