-
2
-
-
39049084399
-
"Primitive quantum BCH codes over finite fields"
-
in Seattle, WA
-
S. A. Aly, A. Klappenecker, and P. K. Sarvepalli, "Primitive quantum BCH codes over finite fields," in Proc. 2006 IEEE Int. Symp. Inf. Theory, Seattle, WA, 2006, pp. 1105-1108.
-
(2006)
Proc. 2006 IEEE Int. Symp. Inf. Theory
, pp. 1105-1108
-
-
Aly, S.A.1
Klappenecker, A.2
Sarvepalli, P.K.3
-
3
-
-
12144260332
-
"A family of quantum stabilizer codes based on the Weyl commutation relations over a finite field"
-
in Cambridge, MA: Birkhäuser, Trends Math
-
V. Arvind and K. R. Parthasarathy, "A family of quantum stabilizer codes based on the Weyl commutation relations over a finite field," in A Tribute to C. S. Seshadri (Chennai, 2002). Cambridge, MA: Birkhäuser, 2003, Trends Math., pp. 133-153.
-
(2003)
A Tribute to C. S. Seshadri (Chennai, 2002)
, pp. 133-153
-
-
Arvind, V.1
Parthasarathy, K.R.2
-
4
-
-
0035504720
-
"Nonbinary quantum stabilizer codes"
-
A. Ashikhmin and E. Knill, "Nonbinary quantum stabilizer codes," IEEE Trans. Inf. Theory, vol. 47, pp. 3065-3072, 2001.
-
(2001)
IEEE Trans. Inf. Theory
, vol.47
, pp. 3065-3072
-
-
Ashikhmin, A.1
Knill, E.2
-
5
-
-
0032656276
-
"Upper bounds on the size of quantum codes"
-
A. Ashikhmin and S. Litsyn, "Upper bounds on the size of quantum codes," IEEE Trans. Inf. Theory, vol. 45, pp. 1206-1215, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 1206-1215
-
-
Ashikhmin, A.1
Litsyn, S.2
-
6
-
-
33646168364
-
"Asymptotically good quantum codes"
-
A. Ashikhmin, M. A. Tsfasman, and S. Litsyn, "Asymptotically good quantum codes," Phys. Rev. A, vol. 63, p. 032311, 2001.
-
(2001)
Phys. Rev. A
, vol.63
, pp. 032311
-
-
Ashikhmin, A.1
Tsfasman, M.A.2
Litsyn, S.3
-
7
-
-
0034188375
-
"Quantum error detection I: Statement of the problem"
-
A. E. Ashikhmin, A. M. Barg, E. Knill, and S. N. Litsyn, "Quantum error detection I: Statement of the problem," IEEE Trans. Inf. Theory, vol. 46, no. 3, pp. 778-788, 2000.
-
(2000)
IEEE Trans. Inf. Theory
, vol.46
, Issue.3
, pp. 778-788
-
-
Ashikhmin, A.E.1
Barg, A.M.2
Knill, E.3
Litsyn, S.N.4
-
8
-
-
0034188124
-
"Quantum error detection II: Bounds"
-
A. E. Ashikhmin, A. M. Barg, E. Knill, and S. N. Litsyn, "Quantum error detection II: Bounds," IEEE Trans. Inf. Theory, vol. 46, no. 3, pp. 789-800, 2000.
-
(2000)
IEEE Trans. Inf. Theory
, vol.46
, Issue.3
, pp. 789-800
-
-
Ashikhmin, A.E.1
Barg, A.M.2
Knill, E.3
Litsyn, S.N.4
-
10
-
-
0000070780
-
"Polynomial codes and finite geometries"
-
in V. S. Pless and W. C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier
-
E. F. Assmus Jr. and J. D. Key, "Polynomial codes and finite geometries," in Handbook of Coding Theory, V. S. Pless and W. C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier, 1998, vol. II, pp. 1269-1343.
-
(1998)
Handbook of Coding Theory
, vol.2
, pp. 1269-1343
-
-
Assmus Jr., E.F.1
Key, J.D.2
-
11
-
-
0034377771
-
"Strengthening the Gilbert-Varshamov bound"
-
A. Barg, S. Guritman, and J. Simonis, "Strengthening the Gilbert-Varshamov bound," Linear Algebra Its Appl., vol. 307, pp. 119-129, 2000.
-
(2000)
Linear Algebra Its Appl.
, vol.307
, pp. 119-129
-
-
Barg, A.1
Guritman, S.2
Simonis, J.3
-
12
-
-
33750592501
-
-
Quantum Message Authentication Codes quant-ph/0103123
-
H. Barnum, Quantum Message Authentication Codes quant-ph/0103123, 2001.
-
(2001)
-
-
Barnum, H.1
-
13
-
-
0036954511
-
"Authentication of quantum messages"
-
H. Barnum, C. Crepeau, D. Gottesman, A. Smith, and A. Tapp, "Authentication of quantum messages," in Proc. 43rd Annu. IEEE Symp. Found. Comput. Sci. (FOCS '02), 2002, pp. 449-458.
-
(2002)
Proc. 43rd Annu. IEEE Symp. Found. Comput. Sci. (FOCS '02)
, pp. 449-458
-
-
Barnum, H.1
Crepeau, C.2
Gottesman, D.3
Smith, A.4
Tapp, A.5
-
14
-
-
0032349883
-
"The quantum Hamming and hexacodes"
-
T. Beth and M. Grassl, "The quantum Hamming and hexacodes," Fortschr. Phys., vol. 46, no. 4-5, pp. 459-491, 1998.
-
(1998)
Fortschr. Phys.
, vol.46
, Issue.4-5
, pp. 459-491
-
-
Beth, T.1
Grassl, M.2
-
15
-
-
0141879417
-
-
Berlin, Germany: Springer-Verlag
-
A. Betten, H. Fripertinger, A. Kerber, A. Wassermann, and K.-H. Zimmermann, Codierungstheorie - Konstruktion und Anwendung Linearer Codes. Berlin, Germany: Springer-Verlag, 1998.
-
(1998)
Codierungstheorie - Konstruktion Und Anwendung Linearer Codes
-
-
Betten, A.1
Fripertinger, H.2
Kerber, A.3
Wassermann, A.4
Zimmermann, K.-H.5
-
16
-
-
0005181969
-
"Quantum twisted codes"
-
J. Bierbrauer and Y. Edel, "Quantum twisted codes," J. Comb. Designs, vol. 8, pp. 174-188, 2000.
-
(2000)
J. Comb. Designs
, vol.8
, pp. 174-188
-
-
Bierbrauer, J.1
Edel, Y.2
-
17
-
-
0004190631
-
-
2nd ed. Providence, RI: Amer. Math. Soc.
-
G. Birkhoff, Lattice Theory, 2nd ed. Providence, RI: Amer. Math. Soc., 1961.
-
(1961)
Lattice Theory
-
-
Birkhoff, G.1
-
18
-
-
0001060859
-
"Quantum error correction and orthogonal geometry"
-
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, "Quantum error correction and orthogonal geometry," Phys. Rev. Lett., vol. 76, pp. 405-409, 1997.
-
(1997)
Phys. Rev. Lett.
, vol.76
, pp. 405-409
-
-
Calderbank, A.R.1
Rains, E.M.2
Shor, P.W.3
Sloane, N.J.A.4
-
19
-
-
0032121784
-
"Quantum error correction via codes over GF(4)"
-
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane, "Quantum error correction via codes over GF(4)," IEEE Trans. Inf. Theory, vol. 44, pp. 1369-1387, 1998.
-
(1998)
IEEE Trans. Inf. Theory
, vol.44
, pp. 1369-1387
-
-
Calderbank, A.R.1
Rains, E.M.2
Shor, P.W.3
Sloane, N.J.A.4
-
20
-
-
0001398327
-
"Good quantum error-correcting codes exist"
-
A. R. Calderbank and P. Shor, "Good quantum error-correcting codes exist," Phys. Rev. A, vol. 54, pp. 1098-1105, 1996.
-
(1996)
Phys. Rev. A
, vol.54
, pp. 1098-1105
-
-
Calderbank, A.R.1
Shor, P.2
-
21
-
-
33750586376
-
-
Constructions and Performance of Classes of Quantum LDPC Codes eprint: Quant-ph/0502086
-
T. Camara, H. Ollivier, and J.-P. Tillich, Constructions and Performance of Classes of Quantum LDPC Codes eprint: Quant-ph/0502086, 2005.
-
(2005)
-
-
Camara, T.1
Ollivier, H.2
Tillich, J.-P.3
-
22
-
-
0000050245
-
"Open problems on cyclic codes"
-
in V. S. Pless and C. W. Huffman, Eds. New York: Elsevier
-
P. Charpin, "Open problems on cyclic codes," in Handbook of Coding Theory, V. S. Pless and C. W. Huffman, Eds. New York: Elsevier, 1998, pp. 963-1063.
-
(1998)
Handbook of Coding Theory
, pp. 963-1063
-
-
Charpin, P.1
-
23
-
-
16944365808
-
"Correcting quantum errors in higher spin systems"
-
H. F. Chau, "Correcting quantum errors in higher spin systems," Phys. Rev. A, vol. 55, pp. R839-R841, 1997.
-
(1997)
Phys. Rev. A
, vol.55
-
-
Chau, H.F.1
-
24
-
-
0004558535
-
"Five quantum register error correction code for higher spin systems"
-
H. F. Chau, "Five quantum register error correction code for higher spin systems," Phys. Rev. A, vol. 56, pp. R1-R4, 1997.
-
(1997)
Phys. Rev. A
, vol.56
-
-
Chau, H.F.1
-
25
-
-
0035397471
-
"Some good quantum error-correcting codes from algebraic-geometric codes"
-
H. Chen, "Some good quantum error-correcting codes from algebraic-geometric codes," IEEE Trans. Inf. Theory, vol. 47, pp. 2059-2061, 2001.
-
(2001)
IEEE Trans. Inf. Theory
, vol.47
, pp. 2059-2061
-
-
Chen, H.1
-
26
-
-
0035395806
-
"Asymptotically good quantum codes exceeding the Ashikhmin-Litsyn-Tsfasman bound"
-
H. Chen, S. Ling, and C. Xing, "Asymptotically good quantum codes exceeding the Ashikhmin-Litsyn-Tsfasman bound," IEEE Trans. Inf. Theory, vol. 47, pp. 2055-2058, 2001.
-
(2001)
IEEE Trans. Inf. Theory
, vol.47
, pp. 2055-2058
-
-
Chen, H.1
Ling, S.2
Xing, C.3
-
27
-
-
4243536108
-
"Quantum stabilizer codes and classical linear codes"
-
R. Cleve, "Quantum stabilizer codes and classical linear codes," Phys. Rev. A, vol. 55, no. 6, pp. 4054-4059, 1997.
-
(1997)
Phys. Rev. A
, vol.55
, Issue.6
, pp. 4054-4059
-
-
Cleve, R.1
-
28
-
-
0010154970
-
"Efficient computations of encodings for quantum error correction"
-
R. Cleve and D. Gottesman, "Efficient computations of encodings for quantum error correction," Phys. Rev. A, vol. 56, no. 1, pp. 76-82, 1997.
-
(1997)
Phys. Rev. A
, vol.56
, Issue.1
, pp. 76-82
-
-
Cleve, R.1
Gottesman, D.2
-
29
-
-
0033320711
-
"On binary constructions of quantum codes"
-
G. Cohen, S. Encheva, and S. Litsyn, "On binary constructions of quantum codes," IEEE Trans. Inf. Theory, vol. 45, pp. 2495-2498, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 2495-2498
-
-
Cohen, G.1
Encheva, S.2
Litsyn, S.3
-
30
-
-
33750579854
-
-
On the Classification of all Self-Dual Additive Codes over GF(4) of Length up to 12 arXiv:math.CO/0504522
-
L. E. Danielsen and M. G. Parker, On the Classification of all Self-Dual Additive Codes over GF(4) of Length up to 12 arXiv:mAth.CO/0504522, 2005.
-
(2005)
-
-
Danielsen, L.E.1
Parker, M.G.2
-
31
-
-
0015357424
-
"Bounds for unrestricted codes by linear programming"
-
P. Delsarte, "Bounds for unrestricted codes by linear programming," Phil. Res. Reports, vol. 27, pp. 272-289, 1972.
-
(1972)
Phil. Res. Reports
, vol.27
, pp. 272-289
-
-
Delsarte, P.1
-
32
-
-
0033875455
-
"Elementary 2-group character codes"
-
C. Ding, D. Kohel, and S. Ling, "Elementary 2-group character codes," IEEE Trans. Inf. Theory, vol. 46, pp. 280-284, 2000.
-
(2000)
IEEE Trans. Inf. Theory
, vol.46
, pp. 280-284
-
-
Ding, C.1
Kohel, D.2
Ling, S.3
-
33
-
-
0000619946
-
"Error correction in quantum communication"
-
A. Ekert and C. Macchiavello, "Error correction in quantum communication," Phys. Rev. Lett., vol. 76, pp. 2585-2588, 1996.
-
(1996)
Phys. Rev. Lett.
, vol.76
, pp. 2585-2588
-
-
Ekert, A.1
Macchiavello, C.2
-
34
-
-
0036672527
-
p (p ≥ 3) exist"
-
p (p ≥ 3) exist," I EEE Trans. Inf. Theory, vo l. 48, pp. 2384-2391, 2002.
-
(2002)
IEEE Trans. Inf. Theory
, vol.48
, pp. 2384-2391
-
-
Feng, K.1
-
36
-
-
10644295697
-
"A finite Gilbert-Varshamov bound for pure stabilizer quantum codes"
-
K. Feng and Z. Ma, "A finite Gilbert-Varshamov bound for pure stabilizer quantum codes," IEEE Trans. Inf. Theory, vol. 50, pp. 3323-3325, 2004.
-
(2004)
IEEE Trans. Inf. Theory
, vol.50
, pp. 3323-3325
-
-
Feng, K.1
Ma, Z.2
-
37
-
-
0005214593
-
"Projective plane and planar quantum codes"
-
M. H. Freedman and D. A. Meyer, "Projective plane and planar quantum codes," Found. Comput. Math., vol. 1, no. 3, pp. 325-332, 2001.
-
(2001)
Found. Comput. Math.
, vol.1
, Issue.3
, pp. 325-332
-
-
Freedman, M.H.1
Meyer, D.A.2
-
38
-
-
0000132422
-
"A class of quantum error-correcting codes saturating the quantum Hamming bound"
-
D. Gottesman, "A class of quantum error-correcting codes saturating the quantum Hamming bound," Phys. Rev. A, vol. 54, pp. 1862-1868, 1996.
-
(1996)
Phys. Rev. A
, vol.54
, pp. 1862-1868
-
-
Gottesman, D.1
-
39
-
-
33750588202
-
-
Pasting Quantum Codes eprint: Quant-ph/9607027
-
D. Gottesman, Pasting Quantum Codes eprint: Quant-ph/9607027, 1996.
-
(1996)
-
-
Gottesman, D.1
-
40
-
-
0003932204
-
"Stabilizer Codes and Quantum Error Correction"
-
Ph.D. dissertation, California Inst. of Technol., Pasadena, CA
-
D. Gottesman, "Stabilizer Codes and Quantum Error Correction," Ph.D. dissertation, California Inst. of Technol., Pasadena, CA, 1997.
-
(1997)
-
-
Gottesman, D.1
-
41
-
-
0033197403
-
"Fault-tolerant quantum computation with higher-dimensional systems"
-
D. Gottesman, "Fault-tolerant quantum computation with higher-dimensional systems," Chaos, Solitons, Fractals, vol. 10, no. 10, pp. 1749-1758, 1999.
-
(1999)
Chaos, Solitons, Fractals
, vol.10
, Issue.10
, pp. 1749-1758
-
-
Gottesman, D.1
-
42
-
-
15844373218
-
"An introduction to quantum error correction"
-
in Providence, RI, eprint: quant-ph/0004072
-
D. Gottesman, "An introduction to quantum error correction," in Proc. Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium, Providence, RI, 2002, pp. 221-235, eprint: quant-ph/0004072.
-
(2002)
Proc. Quantum Computation: A Grand Mathematical Challenge for the Twenty-First Century and the Millennium
, pp. 221-235
-
-
Gottesman, D.1
-
43
-
-
33750582891
-
-
Quantum Error Correction and Fault-Tolerance eprint: quant-ph/0507174
-
D. Gottesman, Quantum Error Correction and Fault-Tolerance eprint: quant-ph/0507174, 2005.
-
(2005)
-
-
Gottesman, D.1
-
44
-
-
33750577236
-
"Algorithmic aspects of error-correcting codes"
-
in R. Brylinski and G. Chen, Eds. Boca Raton, FL: CRC Press
-
M. Grassl, "Algorithmic aspects of error-correcting codes," in The Mathematics of Quantum Computing, R. Brylinski and G. Chen, Eds. Boca Raton, FL: CRC Press, 2001, pp. 223-252.
-
(2001)
The Mathematics of Quantum Computing
, pp. 223-252
-
-
Grassl, M.1
-
45
-
-
0347721141
-
"Quantum BCH codes"
-
in Magdeburg, Germany
-
M. Grassl and T. Beth, "Quantum BCH codes," in Proc. X. Int. Symp. Theoretic. Elec. Eng.,, Magdeburg, Germany, 1999, pp. 207-212.
-
(1999)
Proc. X. Int. Symp. Theoretic. Elec. Eng.
, pp. 207-212
-
-
Grassl, M.1
Beth, T.2
-
46
-
-
25144456293
-
"Cyclic quantum error-correcting codes and quantum shift registers"
-
M. Grassl and T. Beth, "Cyclic quantum error-correcting codes and quantum shift registers," Proc. Royal Soc. London Series A, vol. 456, no. 2003, pp. 2689-2706, 2000.
-
(2000)
Proc. Royal Soc. London Series A
, vol.456
, Issue.2003
, pp. 2689-2706
-
-
Grassl, M.1
Beth, T.2
-
47
-
-
0001979587
-
"Codes for the quantum erasure channel"
-
M. Grassl, T. Beth, and T. Pellizzari, "Codes for the quantum erasure channel," Phys. Rev. Lett. A, vol. 56, no. 1, pp. 33-38, 1997.
-
(1997)
Phys. Rev. Lett. A
, vol.56
, Issue.1
, pp. 33-38
-
-
Grassl, M.1
Beth, T.2
Pellizzari, T.3
-
48
-
-
5044245392
-
"On optimal quantum codes"
-
M. Grassl, T. Beth, and M. Rötteler, "On optimal quantum codes," Int. J. Quantum Inf., vol. 2, no. 1, pp. 757-775, 2004.
-
(2004)
Int. J. Quantum Inf.
, vol.2
, Issue.1
, pp. 757-775
-
-
Grassl, M.1
Beth, T.2
Rötteler, M.3
-
49
-
-
84957679077
-
"Quantum Reed-Solomon codes"
-
in Berlin, Germany: Springer, Lecture Notes in Comput. Sci. (Honolulu, HI, 1999)
-
M. Grassl, W. Geiselmann, and T. Beth, "Quantum Reed-Solomon codes," in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Honolulu, HI, 1999). Berlin, Germany: Springer, 1999, vol. 1719, Lecture Notes in Comput. Sci., pp. 231-244.
-
(1999)
Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
, vol.1719
, pp. 231-244
-
-
Grassl, M.1
Geiselmann, W.2
Beth, T.3
-
50
-
-
84892733534
-
"Efficient quantum circuits for non-qubit quantum error-correcting codes"
-
M. Grassl, M. Rötteler, and T. Beth, "Efficient quantum circuits for non-qubit quantum error-correcting codes," Int. J. Found. Comput. Sci., vol. 14, no. 5, pp. 757-775, 2003.
-
(2003)
Int. J. Found. Comput. Sci.
, vol.14
, Issue.5
, pp. 757-775
-
-
Grassl, M.1
Rötteler, M.2
Beth, T.3
-
51
-
-
0003558781
-
-
ser. Graduate Studies in Mathematics. Providence, RI: Amer. Math. Soc
-
L. C. Grove, Classical Groups and Geometric Algebra, ser. Graduate Studies in Mathematics. Providence, RI: Amer. Math. Soc., 2001.
-
(2001)
Classical Groups and Geometric Algebra
-
-
Grove, L.C.1
-
54
-
-
84894320743
-
"New generalizations of the Reed-Muller codes part I: Primitive codes"
-
T. Kasami, S. Lin, and W. W. Peterson, "New generalizations of the Reed-Muller codes part I: Primitive codes," IEEE Trans. Inf. Theory, vol. 14, pp. 189-199, 1968.
-
(1968)
IEEE Trans. Inf. Theory
, vol.14
, pp. 189-199
-
-
Kasami, T.1
Lin, S.2
Peterson, W.W.3
-
55
-
-
33750581568
-
"New quantum-error-correcting codes from Hermitian self-orthogonal codes over GF(4)"
-
in Oaxaca, Mexico, May 21-25
-
J.-L. Kim, "New quantum-error-correcting codes from Hermitian self-orthogonal codes over GF(4)," in Proc. Sixth Int. Conf. Finite Fields Appl., Oaxaca, Mexico, May 21-25, 2002, pp. 209-213.
-
(2002)
Proc. Sixth Int. Conf. Finite Fields Appl.
, pp. 209-213
-
-
Kim, J.-L.1
-
56
-
-
0141924300
-
"Designs in additive codes over GF(4)"
-
J.-L. Kim and V. Pless, "Designs in additive codes over GF(4)," Designs, Codes, Crypt., vol. 30, pp. 187-199, 2003.
-
(2003)
Designs, Codes, Crypt.
, vol.30
, pp. 187-199
-
-
Kim, J.-L.1
Pless, V.2
-
58
-
-
0040052002
-
"Quantum computations: Algorithms and error correction"
-
A. Y. Kitaev, "Quantum computations: Algorithms and error correction," Russian Math. Surv., vol. 52, no. 6, pp. 1191-1249, 1997.
-
(1997)
Russian Math. Surv.
, vol.52
, Issue.6
, pp. 1191-1249
-
-
Kitaev, A.Y.1
-
59
-
-
0036671294
-
"Beyond stabilizer codes II: Clifford codes"
-
A. Klappenecker and M. Rötteler, "Beyond stabilizer codes II: Clifford codes," IEEE Trans. Inf. Theory, vol. 48, no. 8, pp. 2396-2399, 2002.
-
(2002)
IEEE Trans. Inf. Theory
, vol.48
, Issue.8
, pp. 2396-2399
-
-
Klappenecker, A.1
Rötteler, M.2
-
60
-
-
33750600656
-
-
Group Representations, Error Bases and Quantum Codes Los Alamos National Laboratory, LAUR-96-2807
-
E. Knill, Group Representations, Error Bases and Quantum Codes Los Alamos National Laboratory, LAUR-96-2807, 1996.
-
(1996)
-
-
Knill, E.1
-
61
-
-
33750579101
-
-
Non-Binary Unitary Error Bases and Quantum Codes Los Alamos National Laboratory, LAUR-96-2717
-
E. Knill, Non-Binary Unitary Error Bases and Quantum Codes Los Alamos National Laboratory, LAUR-96-2717, 1996.
-
(1996)
-
-
Knill, E.1
-
62
-
-
14844362515
-
"A theory of quantum error-correcting codes"
-
E. Knill and R. Laflamme, "A theory of quantum error-correcting codes," Phys. Rev. A, vol. 55, no. 2, pp. 900-911, 1997.
-
(1997)
Phys. Rev. A
, vol.55
, Issue.2
, pp. 900-911
-
-
Knill, E.1
Laflamme, R.2
-
63
-
-
0025432647
-
"The weights of the orthogonals of the extended quadratic binary Goppa codes"
-
G. Lachaud and J. Wolfmann, "The weights of the orthogonals of the extended quadratic binary Goppa codes," IEEE Trans. Inf. Theory, vol. 36, pp. 686-692, 1990.
-
(1990)
IEEE Trans. Inf. Theory
, vol.36
, pp. 686-692
-
-
Lachaud, G.1
Wolfmann, J.2
-
64
-
-
0029378543
-
"Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces"
-
V. I. Levenshtein, "Krawtchouk polynomials and universal bounds for codes and designs in Hamming spaces," IEEE Trans. Inf. Theory, vol. 41, pp. 1303-1321, 1995.
-
(1995)
IEEE Trans. Inf. Theory
, vol.41
, pp. 1303-1321
-
-
Levenshtein, V.I.1
-
65
-
-
2942640141
-
"Binary construction of quantum codes of minimum distance three and four"
-
R. Li and X. Li, "Binary construction of quantum codes of minimum distance three and four," IEEE Trans. Inf. Theory, vol. 50, pp. 1331-1336, 2004.
-
(2004)
IEEE Trans. Inf. Theory
, vol.50
, pp. 1331-1336
-
-
Li, R.1
Li, X.2
-
66
-
-
5144233236
-
"Sparse-graph codes for quantum error correction"
-
D. J. C. MacKay, G. Mitchison, and P. L. McFadden, "Sparse-graph codes for quantum error correction," IEEE Trans. Inf. Theory, vol. 50, pp. 2315-2330, 2004.
-
(2004)
IEEE Trans. Inf. Theory
, vol.50
, pp. 2315-2330
-
-
MacKay, D.J.C.1
Mitchison, G.2
McFadden, P.L.3
-
67
-
-
0002627993
-
"A theorem on the distribution of weights in a systematic code"
-
F. J. MacWilliams, "A theorem on the distribution of weights in a systematic code," Bell Syst. Tech. J., vol. 42, pp. 79-94, 1963.
-
(1963)
Bell Syst. Tech. J.
, vol.42
, pp. 79-94
-
-
MacWilliams, F.J.1
-
69
-
-
2442563746
-
"A physics-free introduction to quantum error correcting codes"
-
W. J. Martin, "A physics-free introduction to quantum error correcting codes," Util. Math., pp. 133-158, 2004.
-
(2004)
Util. Math.
, pp. 133-158
-
-
Martin, W.J.1
-
70
-
-
0036649704
-
"Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes"
-
R. Matsumoto, "Improvement of Ashikhmin-Litsyn-Tsfasman bound for quantum codes," IEEE Trans. Inf. Theory, vol. 48, pp. 2122-2124, 2002.
-
(2002)
IEEE Trans. Inf. Theory
, vol.48
, pp. 2122-2124
-
-
Matsumoto, R.1
-
71
-
-
0034294361
-
m-state systems from classical error correcting codes"
-
m-state systems from classical error correcting codes," IEICE Trans. Fund., vol. E83-A, no. 10, pp. 1878-1883, 2000.
-
(2000)
IEICE Trans. Fund.
, vol.E83-A
, Issue.10
, pp. 1878-1883
-
-
Matsumoto, R.1
Uyematsu, T.2
-
72
-
-
0017468074
-
"New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities"
-
R. J. McEliece, E. R. Rodemich jr., H. Rumsey, and L. R. Welch, "New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities," IEEE Trans. Inf. Theory, vol. 23, p. 157, 1977.
-
(1977)
IEEE Trans. Inf. Theory
, vol.23
, pp. 157
-
-
McEliece, R.J.1
Rodemich Jr., E.R.2
Rumsey, H.3
Welch, L.R.4
-
73
-
-
0028547520
-
"The Macwilliams-sloane conjecture on the tightness of the Carlitz-Uchiyama bound and the weights of the duals of BCH codes"
-
O. Moreno and C. J. Moreno, "The Macwilliams-sloane conjecture on the tightness of the Carlitz-Uchiyama bound and the weights of the duals of BCH codes," IEEE Trans. Inf. Theory, vol. 40, pp. 1894-1907, 1994.
-
(1994)
IEEE Trans. Inf. Theory
, vol.40
, pp. 1894-1907
-
-
Moreno, O.1
Moreno, C.J.2
-
75
-
-
0000580989
-
"Galois connexions"
-
O. Ore, "Galois connexions," Trans. Amer. Math. Soc., vol. 55, pp. 493-513, 1944.
-
(1944)
Trans. Amer. Math. Soc.
, vol.55
, pp. 493-513
-
-
Ore, O.1
-
76
-
-
1942454247
-
"List decoding of q-ary Reed-Muller codes"
-
R. Pellikaan and X.-W. Wu, "List decoding of q-ary Reed-Muller codes," IEEE Trans. Inform. Theory, vol. 50, pp. 679-682, 2004.
-
(2004)
IEEE Trans. Inform. Theory
, vol.50
, pp. 679-682
-
-
Pellikaan, R.1
Wu, X.-W.2
-
77
-
-
33750584988
-
-
A Proposed Quantum Low Density Parity Check Code eprint: quant-ph/ 0108131
-
M. S. Postol, A Proposed Quantum Low Density Parity Check Code eprint: quant-ph/0108131, 2001.
-
(2001)
-
-
Postol, M.S.1
-
78
-
-
0032124004
-
"Quantum weight enumerators"
-
E. M. Rains, "Quantum weight enumerators," IEEE Trans. Inf. Theory, vol. 44, pp. 1388-1394, 1998.
-
(1998)
IEEE Trans. Inf. Theory
, vol.44
, pp. 1388-1394
-
-
Rains, E.M.1
-
79
-
-
0033328407
-
"Monotonicity of the quantum linear programming bound"
-
E. M. Rains, "Monotonicity of the quantum linear programming bound," IEEE Trans. Inf. Theory, vol. 45, pp. 2489-2492, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 2489-2492
-
-
Rains, E.M.1
-
80
-
-
0033184975
-
"Nonbinary quantum codes"
-
E. M. Rains, "Nonbinary quantum codes," IEEE Trans. Inf. Theory, vol. 45, pp. 1827-1832, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 1827-1832
-
-
Rains, E.M.1
-
81
-
-
0032679721
-
"Quantum codes of minimum distance two"
-
E. M. Rains, "Quantum codes of minimum distance two," IEEE Trans. Inf. Theory, vol. 45, pp. 266-271, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 266-271
-
-
Rains, E.M.1
-
82
-
-
0033344877
-
"Quantum shadow enumerators"
-
E. M. Rains, "Quantum shadow enumerators," IEEE Trans. Inf. Theory, vol. 45, pp. 2361-2366, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 2361-2366
-
-
Rains, E.M.1
-
83
-
-
0033882817
-
"Polynomial invariants of quantum codes"
-
E. M. Rains, "Polynomial invariants of quantum codes," IEEE Trans. Inf. Theory, vol. 46, pp. 54-59, 2000.
-
(2000)
IEEE Trans. Inf. Theory
, vol.46
, pp. 54-59
-
-
Rains, E.M.1
-
84
-
-
5044251357
-
"On quantum MDS codes"
-
in Chicago, USA
-
M. Rötteler, M. Grassl, and T. Beth, "On quantum MDS codes," in Proc. 2004 IEEE Int. Symp. Inf. Theory, Chicago, USA, 2004, p. 355.
-
(2004)
Proc. 2004 IEEE Int. Symp. Inf. Theory
, pp. 355
-
-
Rötteler, M.1
Grassl, M.2
Beth, T.3
-
85
-
-
84941262196
-
"Nonbinary quantum Reed-Muller codes"
-
in Adelaide, Australia
-
P. K. Sarvepalli and A. Klappenecker, "Nonbinary quantum Reed-Muller codes," in Proc. 2005 IEEE Int. Symp. Inf. Theory, Adelaide, Australia, 2005, pp. 1023-1027.
-
(2005)
Proc. 2005 IEEE Int. Symp. Inf. Theory
, pp. 1023-1027
-
-
Sarvepalli, P.K.1
Klappenecker, A.2
-
86
-
-
0242634028
-
"Stabilizer codes can be realized as graph codes"
-
D. Schlingemann, "Stabilizer codes can be realized as graph codes," Quantum Inf. Comput., vol. 2, no. 4, pp. 307-323, 2002.
-
(2002)
Quantum Inf. Comput.
, vol.2
, Issue.4
, pp. 307-323
-
-
Schlingemann, D.1
-
87
-
-
33750585287
-
-
Quantum Error-Correcting Codes Associated with Graphs eprint: quant-ph/ 00012111
-
D. Schlingemann and R. F. Werner, Quantum Error-Correcting Codes Associated with Graphs eprint: Quant-ph/00012111, 2000.
-
(2000)
-
-
Schlingemann, D.1
Werner, R.F.2
-
88
-
-
84967743304
-
"Families of curves and weight distributions of codes"
-
R. Schoof, "Families of curves and weight distributions of codes," Bull. Amer. Math. Soc., vol. 32, no. 2, pp. 171-183, 1995.
-
(1995)
Bull. Amer. Math. Soc.
, vol.32
, Issue.2
, pp. 171-183
-
-
Schoof, R.1
-
89
-
-
84968476225
-
"Weight formulas for ternary Melas codes"
-
R. Schoof, G. van der Geer, and M. van der Vlugt, "Weight formulas for ternary Melas codes," Math. Comp., vol. 58, pp. 781-792, 1992.
-
(1992)
Math. Comp.
, vol.58
, pp. 781-792
-
-
Schoof, R.1
van der Geer, G.2
van der Vlugt, M.3
-
90
-
-
0041979610
-
"Factorization of symmetric matrices and trace-orthogonal bases in finite fields"
-
G. Seroussi and A. Lempel, "Factorization of symmetric matrices and trace-orthogonal bases in finite fields," SIAM J. Comput., vol. 9, pp. 758-767, 1980.
-
(1980)
SIAM J. Comput.
, vol.9
, pp. 758-767
-
-
Seroussi, G.1
Lempel, A.2
-
91
-
-
33746738958
-
"Scheme for reducing decoherence in quantum memory"
-
P. Shor, "Scheme for reducing decoherence in quantum memory," Phys. Rev. A, vol. 2, pp. 2493-2496, 1995.
-
(1995)
Phys. Rev. A
, vol.2
, pp. 2493-2496
-
-
Shor, P.1
-
92
-
-
0001267593
-
"Quantum analog of the MacWilliams identities in classical coding theory"
-
P. Shor and R. Laflamme, "Quantum analog of the MacWilliams identities in classical coding theory," Phys. Rev. Lett., vol. 78, pp. 1600-1603, 1997.
-
(1997)
Phys. Rev. Lett.
, vol.78
, pp. 1600-1603
-
-
Shor, P.1
Laflamme, R.2
-
93
-
-
0032675420
-
"Quantum Reed-Muller codes"
-
A. Steane, "Quantum Reed-Muller codes," IEEE Trans. Inf. Theory, vol. 45, pp. 1701-1703, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 1701-1703
-
-
Steane, A.1
-
94
-
-
0007244732
-
"Multiple-particle interference and quantum error correction"
-
A. M. Steane, "Multiple-particle interference and quantum error correction," Proc. Roy. Soc. London A, vol. 452, pp. 2551-2577, 1996.
-
(1996)
Proc. Roy. Soc. London A
, vol.452
, pp. 2551-2577
-
-
Steane, A.M.1
-
95
-
-
4043092517
-
"Simple quantum error correcting codes"
-
A. M. Steane, "Simple quantum error correcting codes," Phys. Rev. Lett., vol. 77, pp. 793-797, 1996.
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 793-797
-
-
Steane, A.M.1
-
96
-
-
0032606638
-
"Enlargement of Calderbank-Shor-Steane quantum codes"
-
A. M. Steane, "Enlargement of Calderbank-Shor-Steane quantum codes," IEEE Trans. Inf. Theory, vol. 45, pp. 2492-2495, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 2492-2495
-
-
Steane, A.M.1
-
97
-
-
0028388695
-
"Generalized Hamming weights of trace codes"
-
H. Stichtenoth and C. Voß, "Generalized Hamming weights of trace codes," IEEE Trans. Inf. Theory, vol. 40, pp. 554-558, 1994.
-
(1994)
IEEE Trans. Inf. Theory
, vol.40
, pp. 554-558
-
-
Stichtenoth, H.1
Voß, C.2
-
99
-
-
0039770773
-
"Generalized Hamming weights of Melas codes and dual Melas codes"
-
G. van der Geer and M. van der Vlugt, "Generalized Hamming weights of Melas codes and dual Melas codes," SIAM J. Disc. Math., vol. 7, no. 4, pp. 554-559, 1980.
-
(1980)
SIAM J. Disc. Math.
, vol.7
, Issue.4
, pp. 554-559
-
-
van der Geer, G.1
van der Vlugt, M.2
-
100
-
-
0032636507
-
"Spatially correlated qubit errors and burst-correcting quantum codes"
-
F. Vatan, V. P. Roychowdhury, and M. P. Anantram, "Spatially correlated qubit errors and burst-correcting quantum codes," IEEE Trans. Inf. Theory, vol. 45, pp. 1703-1708, 1999.
-
(1999)
IEEE Trans. Inf. Theory
, vol.45
, pp. 1703-1708
-
-
Vatan, F.1
Roychowdhury, V.P.2
Anantram, M.P.3
-
101
-
-
1842533569
-
"Quantum cyclic and constacyclic codes"
-
L. Xiaoyan, "Quantum cyclic and constacyclic codes," IEEE Trans. Inf. Theory, vol. 50, pp. 547-549, 2004.
-
(2004)
IEEE Trans. Inf. Theory
, vol.50
, pp. 547-549
-
-
Xiaoyan, L.1
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