A Group-Theoretic Framework for the Construction of Packings in Grassmannian Spaces
A.R. Calderbank
, R.H. Hardin
, E.M. Rains
, P.W. Shor
and N.J.A. Sloane
DOI: 10.1023/A:1018673825179
Abstract
By using totally isotropic subspaces in an orthogonal space 
+ (2i, 2), several infinite families of packings of 2k-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.
+ (2i, 2), several infinite families of packings of 2k-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.Pages: 129–140
Keywords: Grassmannian packings; quantum computing; orthogonal geometry; Clifford group
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References
1. D. Applegate and D.S. Johnson, personal communication,
1993. Their programs can be obtained from
1993. Their programs can be obtained from