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

2002/08/01 by A. R. Calderbank, R. H. Hardin, E. M. Rains +2
Mathematics · #math.CO #msc:51E15

paper · pdf

published as J. Algebraic Combinatorics, 9 (1999), 129-140 · 15 pages

arxiv created 2002/08/01 · arxiv updated 2009/11/30

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 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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