## DIMACS TR: 2000-19

## Bounds for Packings of Spheres in the Grassmann Manifolds

### Authors: A. Barg, D. Nogin

**
ABSTRACT
**

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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