A group-theoretic framework for the construction of packings in Grassmannian spaces

Calderbank, A.R.; Hardin, R.H.; Rains, E.M.; Shor, P.W.; Sloane, N.J.A.

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A group-theoretic framework for the construction of packings in Grassmannian spaces

Calderbank, A.R. ; Hardin, R.H. ; Rains, E.M. ; Shor, P.W. ; Sloane, N.J.A.

Journal of Algebraic Combinatorics, Tome 9 (1999) no. 2, pp. 129-140.

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Résumé

Summary: By using totally isotropic subspaces in an orthogonal space $OHgr$+ (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.

Keywords: Grassmannian packings, quantum computing, orthogonal geometry, Clifford group

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     title = {A group-theoretic framework for the construction of packings in {Grassmannian} spaces},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_1999__9_2_a5/}
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Calderbank, A.R.; Hardin, R.H.; Rains, E.M.; Shor, P.W.; Sloane, N.J.A. A group-theoretic framework for the construction of packings in Grassmannian spaces. Journal of Algebraic Combinatorics, Tome 9 (1999) no. 2, pp. 129-140. http://geodesic.mathdoc.fr/item/JAC_1999__9_2_a5/