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Bounds on Packings of Spheres in the Grassmann Manifolds

01 September 2002

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We derive the Varshamov-Gilbert and Hamming bounds for packings of spheres (codes) in the Grassmann manifolds over R and C. The distance between two k-planes is defined as p(p,q)=(sin sup 2 theta sub 1 +...+ sin sup 2 theta sub k) sup (1/2), where theta sub i, 1 <= i <= k, are the principal angles between p and q.