DIMACS TR: 2000-19

Bounds for Packings of Spheres in the Grassmann Manifolds

Authors: A. Barg, D. Nogin


We derive the Varshamov--Gilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over $\mathbb R$ and $\mathbb C$. The distance between two $k$-planes is defined as $\rho(p,q)=(\sin^2\theta_1+\dots+\sin^2\theta_k)^{1/2}$, where $\theta_i, 1\le i\le k$, are the principal angles between $p$ and $q$.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2000/2000-19.ps.gz
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