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Quantum Error Correction Via Codes Over GF(4) (1997)

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by A. R. Calderbank , E. M. Rains , P. W. Shor , N. J. A. Sloane
Citations:204 - 16 self
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@MISC{Calderbank97quantumerror,
    author = {A. R. Calderbank and E. M. Rains and P. W. Shor and N. J. A. Sloane},
    title = {Quantum Error Correction Via Codes Over GF(4) },
    year = {1997}
}

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Abstract

The problem of finding quantum-error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are presented, as well as a table of upper and lower bounds on such codes of length up to 30 qubits.

Citations

1605 The Theory of Error-Correcting Codes - MacWilliams, Sloane - 1978
455 The MAGMA Algebra System I: The User Language - Bosma, Cannon, et al. - 1997
386 Basic Algebra - Jacobson - 1974
365 Teleporting an unknown quantum state via dual classical and EPR channels," Phys - Bennett, Brassard, et al. - 1993
310 AMPL: A Modeling Language for - Fourer, Gay, et al. - 1993
236 Good quantum error-correcting codes exist,” Phys - Calderbank, Shor
228 Introduction to Coding Theory - Lint - 1999
220 Endliche Gruppen I - Huppert - 1967
180 Fault-tolerant quantum computation - Shor
174 Fault-tolerant quantum computation with constant error - Aharonov, Ben-Or - 1997
148 Mixed state entanglement and quantum error correction - Bennett, DiVincenzo, et al. - 1996
142 A class of quantum error-correcting codes saturating the quantum Hamming bound,” lanl e-print quant-ph/9604038 - Gottesman
129 Perfect quantum error correction code,” lanl e-print quant-ph/9602019 - Laflamme, Miquel, et al.
128 Multiple particle interference and quantum error correction - Steane
117 A single quantum cannot be cloned - Wootters, Zurek - 1982
113 Handbook of Magma Functions - Bosma, Cannon - 1995
92 Quantum error correction and orthogonal geometry,” lanl e-print quant-ph/9605005 - Calderbank, Rains, et al.
78 Scheme for reducing decoherence in quantum memory,” Phys - Shor - 1995
68 Packing lines, planes, etc.: packings in Grassmannian space - Conway, Hardin, et al. - 1996
63 A nonadditive quantum code - Rains, Hardin, et al. - 1997
56 Bounds for unrestricted codes, by linear programming - Delsarte - 1972
51 Finite Group Theory - Aschbacher - 1986
47 Non-binary unitary error bases and quantum codes," LANL e-print quantph /9608037 - Knill
43 A new upper bound on the minimal distance of self-dual codes - Conway, Sloane - 1990
43 Communication by EPR devices - Dieks - 1982
43 Quantum channel capacity of very noisy channels,” Phys - DiVincenzo, Shor, et al. - 1998
38 Group representations, error bases and quantum codes," LANL e-print quantph /9608048 - Knill
37 Fault-tolerant error correction with efficient quantum codes - DiVincenzo, Shor - 1996
36 Quantum analog of the MacWilliams identities in classical coding theory - Shor, Laflamme - 1997
29 The geometry of two-weight codes - Calderbank, Kantor - 1986
29 An upper bound for self-dual codes - Mallows, Sloane - 1973
29 Shadow bounds for self-dual codes - Rains
28 Simple quantum error correcting codes - Steane
27 Efficient computations of encodings for quantum error correction - Cleve, Gottesman - 1997
26 A group-theoretic framework for the construction of packings in Grassmannian spaces - Calderbank, Hardin, et al. - 1997
22 Threshold accuracy for quantum computation," LANL e-print quant-ph/9610011 - Knill, Laflamme, et al.
21 Z 4 Kerdock codes, orthogonal spreads, and extremal Euclidean line-sets - Calderbank, Cameron, et al.
20 Self-dual codes over GF (4 - MacWilliams, Odlyzko, et al. - 1978
20 time, parallelism and noise requirements for reliable quantum computing," LANL e-print quant-ph/9708021 - Steane, Space
18 On Clifford collineation, transform and similarity groups - Bolt, Room, et al. - 1961
16 Some ternary and quaternary codes and associated sphere packings - Kschischang, Pasupathy - 1992
15 Self-dual codes over GF (3) and GF (4) of length not exceeding 16 - Conway, Pless, et al. - 1979
15 Self-dual codes and lattices - Sloane - 1979
13 Programming with algebraic structures: Design of the Magma language - Bosma, Cannon, et al. - 1994
13 Quantum stabilizer codes and classical linear codes," LANL e-print quantph /9612048 - Cleve
12 Error correction in quantum communication - Ekert, Macchiavello - 1996
11 A family of optimal packings in Grassmannian manifolds - Shor, Sloane - 1997
10 A 2-adic approach to the analysis of cyclic codes - Calderbank, Li, et al. - 1997
10 personal communication - Kitaev - 1997
9 On Clifford collineation, transform and similarity groups - Wall - 1962
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