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A GroupTheoretic Framework for the Construction of Packings in Grassmannian Spaces
, 2002
"... By using totally isotropic subspaces in an orthogonal space Ω + (2i,2), several infinite families of packings of 2 kdimensional subspaces of real 2 idimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this ..."
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Cited by 40 (11 self)
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By using totally isotropic subspaces in an orthogonal space Ω + (2i,2), several infinite families of packings of 2 kdimensional subspaces of real 2 idimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with BarnesWall lattices, Kerdock sets and quantumerrorcorrecting codes.
Geometric structures arising from generalized jplanes
, 2009
"... We study translation planes constructed by Andre ́ net replacement on jj · · · jplanes and derivation on jj · · · jplanes. Then, we get to the conclusion that the family of nonAndre ́ jj · · · jplanes is new, and thus so are their replaced and derived planes. We also study a new way to c ..."
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We study translation planes constructed by Andre ́ net replacement on jj · · · jplanes and derivation on jj · · · jplanes. Then, we get to the conclusion that the family of nonAndre ́ jj · · · jplanes is new, and thus so are their replaced and derived planes. We also study a new way to construct translation planes by putting together two ‘halves’ of planes that belong to two different jj · · · jplanes. We show examples of planes of small order constructed this way. Finally, we prove that using regular hyperbolic covers, jj · · · jplanes induce partitions of Segre varieties by Veronesians (sometimes called flat flocks)
A GroupTheoretic Framework for the Construction of Packings in Grassmannian Spaces
, 1997
"... Abstract. By using totally isotropic subspaces in an orthogonal space � +(2i, 2), several infinite families of packings of 2kdimensional subspaces of real 2idimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and li ..."
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Abstract. By using totally isotropic subspaces in an orthogonal space � +(2i, 2), several infinite families of packings of 2kdimensional subspaces of real 2idimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with BarnesWall lattices, Kerdock sets and quantumerrorcorrecting codes. Keywords: Grassmannian packings, quantum computing, orthogonal geometry, Clifford group