Bounds on Packings of Spheres in the Grassmann Manifolds
01 September 2002
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.