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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
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Abstract

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.

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A. R. Calderbank, R. H. Hardin, E. M. Rains, P. W. Shor, N. J. A. Sloane. 2002-08-01. A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces. https://arxiv.org/abs/math/0208002

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