218
References
16. Berlekamp, E.R.: Negacyclic codes for the Lee metric. In: Symposium on Combinatorial
Mathematics and Its Applications, North Carolina, USA, 10–14 April 1967
17. Bierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. Des. 8, 174–188 (2000)
18. Blackford, T.: Negacyclic duadic codes. Finite Fields Appl. 14, 930–943 (2008)
19. Blahut, R.E.: Algebraic Codes for Data Transmission. Cambridge University Press, New York,
USA (2003)
20. Bombin, H., Martin-Delgado, M.A.: Topological quantum error correction with optimal
encoding rate. Phys. Rev. A 73, 062303-1–062303-5 (2006)
21. Bombin, H., Martin-Delgado, M.A.: Topological quantum distillation. Phys. Rev. Lett. 97,
180501-1-1–180501-4 (2006)
22. Bose, R.C., Ray-Chaudhuri, D.K.: On a class of error correcting binary group codes. Inf.
Control 3, 68–79 (1960)
23. Bose, R.C., Ray-Chaudhuri, D.K.: Further results on error correcting binary group codes. Inf.
Control 3, 279–290 (1960)
24. Buchbinder, S.D., Huang, C.L., Weinstein, Y.S.: Encoding an arbitrary state in a [7, 1, 3]
quantum error correction code. Quantum Inf. Process. 12, 699–719 (2013)
25. Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via
codes over G F(4). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)
26. Chen, H.: Some good quantum error-correcting codes from algebraic-geometric codes. IEEE
Trans. Inf. Theory 47, 2059–2061 (2001)
27. Chen, H., Ling, S., Xing, C.: Asymptotically good quantum codes exceeding the AshikhminLitsyn-Tsfasman bound. IEEE Trans. Inf. Theory 47, 2055–2058 (2001)
28. Chen, H., Ling, S., Xing, C.: Quantum codes from concatenated algebraic-geometric codes.
IEEE Trans. Inf. Theory 51, 2915–2920 (2005)
29. Climent, J.J., Herranz, V., Perea.: Linear system modelization of concatenated block and
convolutional codes. Linear Algebra Appl. 429, 1191–1212 (2008)
30. Cohen, G.D., Encheva, S.B., Litsyn, S.: On binary constructions of quantum codes. IEEE
Trans. Inf. Theory 45, 2495–2498 (1999)
31. Curto, J.I., Porras, J.M., Martín, F.J.P., Sotelo, G.S.: Convolutional Goppa codes defined on
fibrations. A.A.E.C.C. 23, 165–178 (2012)
32. de Almeida, A.C.A., Palazzo Jr., R.: A concatenated [(4, 1, 3)] quantum convolutional code.
In: IEEE Information Theory Workshop (ITW), San Antonio, Texas, 28–33 Oct 2004
33. Ding, C., Kohel, D., Ling, S.: Elementary 2-group character codes. IEEE Trans. Inf. Theory
46, 280–284 (2000)
34. Edel, Y.: Table of quantum twisted codes. Electronic address: www.mathi.uni-heidelberg.de/
~yves/Matritzen/QTBCH/QTBCHIndex.html
35. Ezerman, M.F., Ling, S., Solé, P.: Additive asymmetric quantum codes. IEEE Trans. Inf.
Theory 57, 5536–5550 (2011)
36. Ezerman, M.F., Ling, S., Yemen, O., Solé, P.: From skew-cyclic codes to asymmetric quantum
codes. Adv. Math. Commun. 5, 41–57 (2011)
37. Ezerman, M.F., Jitman, S., Ling, S.: Pure asymmetric quantum MDS codes from CSS construction: a complete characterization. Int. J. Quantum Inf. 11(1350027), 1–10 (2013)
38. Feng, K., Ma, Z.: A finite Gilbert-Varshamov bound for pure stabilizer quantum codes. IEEE
Trans. Inf. Theory 50, 3323–3325 (2004)
39. Feng, K., Ling, S., Xing, C.: Asymptotic bounds on quantum codes from algebraic geometry
codes. IEEE Trans. Inf. Theory 52, 986–991 (2006)
40. Forney Jr., G.D.: Convolutional codes I: algebraic structure. IEEE Trans. Inf. Theory 16,
720–738 (1970)
41. Forney Jr., G.D., Grassl, M., Guha, S.: Convolutional and tail-biting quantum error-correcting
codes. IEEE Trans. Inf. Theory 53, 865–880 (2007)
42. Fujiwara, Y.: Block synchronization for quantum information. Phys. Rev. A 87, 23–44 (2013)
43. Fujiwara, Y., Tonchev, V.D., Wong, T.W.H.: Algebraic techniques in designing quantum synchronizable codes. Phys. Rev. A 88, 012318 (2013)
References
16. Berlekamp, E.R.: Negacyclic codes for the Lee metric. In: Symposium on Combinatorial
Mathematics and Its Applications, North Carolina, USA, 10–14 April 1967
17. Bierbrauer, J., Edel, Y.: Quantum twisted codes. J. Comb. Des. 8, 174–188 (2000)
18. Blackford, T.: Negacyclic duadic codes. Finite Fields Appl. 14, 930–943 (2008)
19. Blahut, R.E.: Algebraic Codes for Data Transmission. Cambridge University Press, New York,
USA (2003)
20. Bombin, H., Martin-Delgado, M.A.: Topological quantum error correction with optimal
encoding rate. Phys. Rev. A 73, 062303-1–062303-5 (2006)
21. Bombin, H., Martin-Delgado, M.A.: Topological quantum distillation. Phys. Rev. Lett. 97,
180501-1-1–180501-4 (2006)
22. Bose, R.C., Ray-Chaudhuri, D.K.: On a class of error correcting binary group codes. Inf.
Control 3, 68–79 (1960)
23. Bose, R.C., Ray-Chaudhuri, D.K.: Further results on error correcting binary group codes. Inf.
Control 3, 279–290 (1960)
24. Buchbinder, S.D., Huang, C.L., Weinstein, Y.S.: Encoding an arbitrary state in a [7, 1, 3]
quantum error correction code. Quantum Inf. Process. 12, 699–719 (2013)
25. Calderbank, A.R., Rains, E.M., Shor, P.W., Sloane, N.J.A.: Quantum error correction via
codes over G F(4). IEEE Trans. Inf. Theory 44, 1369–1387 (1998)
26. Chen, H.: Some good quantum error-correcting codes from algebraic-geometric codes. IEEE
Trans. Inf. Theory 47, 2059–2061 (2001)
27. Chen, H., Ling, S., Xing, C.: Asymptotically good quantum codes exceeding the AshikhminLitsyn-Tsfasman bound. IEEE Trans. Inf. Theory 47, 2055–2058 (2001)
28. Chen, H., Ling, S., Xing, C.: Quantum codes from concatenated algebraic-geometric codes.
IEEE Trans. Inf. Theory 51, 2915–2920 (2005)
29. Climent, J.J., Herranz, V., Perea.: Linear system modelization of concatenated block and
convolutional codes. Linear Algebra Appl. 429, 1191–1212 (2008)
30. Cohen, G.D., Encheva, S.B., Litsyn, S.: On binary constructions of quantum codes. IEEE
Trans. Inf. Theory 45, 2495–2498 (1999)
31. Curto, J.I., Porras, J.M., Martín, F.J.P., Sotelo, G.S.: Convolutional Goppa codes defined on
fibrations. A.A.E.C.C. 23, 165–178 (2012)
32. de Almeida, A.C.A., Palazzo Jr., R.: A concatenated [(4, 1, 3)] quantum convolutional code.
In: IEEE Information Theory Workshop (ITW), San Antonio, Texas, 28–33 Oct 2004
33. Ding, C., Kohel, D., Ling, S.: Elementary 2-group character codes. IEEE Trans. Inf. Theory
46, 280–284 (2000)
34. Edel, Y.: Table of quantum twisted codes. Electronic address: www.mathi.uni-heidelberg.de/
~yves/Matritzen/QTBCH/QTBCHIndex.html
35. Ezerman, M.F., Ling, S., Solé, P.: Additive asymmetric quantum codes. IEEE Trans. Inf.
Theory 57, 5536–5550 (2011)
36. Ezerman, M.F., Ling, S., Yemen, O., Solé, P.: From skew-cyclic codes to asymmetric quantum
codes. Adv. Math. Commun. 5, 41–57 (2011)
37. Ezerman, M.F., Jitman, S., Ling, S.: Pure asymmetric quantum MDS codes from CSS construction: a complete characterization. Int. J. Quantum Inf. 11(1350027), 1–10 (2013)
38. Feng, K., Ma, Z.: A finite Gilbert-Varshamov bound for pure stabilizer quantum codes. IEEE
Trans. Inf. Theory 50, 3323–3325 (2004)
39. Feng, K., Ling, S., Xing, C.: Asymptotic bounds on quantum codes from algebraic geometry
codes. IEEE Trans. Inf. Theory 52, 986–991 (2006)
40. Forney Jr., G.D.: Convolutional codes I: algebraic structure. IEEE Trans. Inf. Theory 16,
720–738 (1970)
41. Forney Jr., G.D., Grassl, M., Guha, S.: Convolutional and tail-biting quantum error-correcting
codes. IEEE Trans. Inf. Theory 53, 865–880 (2007)
42. Fujiwara, Y.: Block synchronization for quantum information. Phys. Rev. A 87, 23–44 (2013)
43. Fujiwara, Y., Tonchev, V.D., Wong, T.W.H.: Algebraic techniques in designing quantum synchronizable codes. Phys. Rev. A 88, 012318 (2013)