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

被引：47

作者：

Calderbank, AR ^{[1
]}

Hardin, RH ^{[1
]}

Rains, EM ^{[1
]}

Shor, PW ^{[1
]}

Sloane, NJA ^{[1
]}

机构：

[1] AT&T Bell Labs, Res, Informat Sci Res, Florham Pk, NJ 07932 USA

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 1999年 / 9卷 / 02期

关键词：

Grassmannian packings; quantum computing; orthogonal geometry; Clifford group;

D O I：

10.1023/A:1018673825179

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using totally isotropic subspaces in an orthogonal space Omega(+)(2i, 2), several infinite families of packings of 2(k) -dimensional subspaces of real 2(i) -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.

引用

页码：129 / 140

页数：12

共 22 条

[1]

APPLEGATE D, 1993, COMMUNICATION

[2]

Aschbacher M., 2000, FINITE GROUP THEORY

[3]

Bennett CH, 1996, PHYS REV A, V54, P3824, DOI 10.1103/PhysRevA.54.3824

[4]

Bolt B., 1961, J AUSTR MATH SOC, V2, P80

[5]

BOLT B, 1961, J AUSTR MATH SOC, V2, P60

[6]

Brouwer A.E., 1989, DISTANCE REGULAR GRA

[7] Z(4)-Kerdock codes, orthogonal spreads, and extremal euclidean line-sets [J].

Calderbank, AR ;

Cameron, PJ ;

Kantor, WM ;

Seidel, JJ .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1997, 75 :436-480

[8] Quantum error correction via codes over GF (4) [J].

Calderbank, AR ;

Rains, EM ;

Shor, PW ;

Sloane, NJA .

IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (04) :1369-1387

[9] Quantum-error correction and orthogonal geometry [J].

Calderbank, AR ;

Rains, EM ;

Shor, PW ;

Sloane, NJA .

PHYSICAL REVIEW LETTERS, 1997, 78 (03) :405-408

[10]

Conway J. H., 1996, EXP MATH, V5, P139

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