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On the performance of binary extremal self-dual codes
1. | Department of Mathematics and Informatics, Veliko Tarnovo University, 5000 Veliko Tarnovo, Bulgaria |
2. | Department of Mathematics, Otto-von-Guericke-University, 39016 Magdeburg, Germany, Germany |
References:
[1] |
C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows, J. Combin. Theory A, 105 (2004), 15-34.
doi: 10.1016/j.jcta.2003.09.003. |
[2] |
S. Bouyuklieva and V. Yorgov, Singly-even codes of length 40, Des. Codes Crypt., 9 (1996), 131-141.
doi: 10.1007/BF00124589. |
[3] |
Y. Cheng and N. J. A. Sloane, Codes from symmetry groups, and a $[32,17,8]$ code, SIAM J. Discrete Math., 2 (1989), 28-37.
doi: 10.1137/0402003. |
[4] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[5] |
R. Doncheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7, Appl. Algebra Eng. Comm. Comp., 14 (2003), 75-79.
doi: 10.1007/s00200-003-0126-4. |
[6] |
A. Faldum, J. Lafuente, G. Ochoa and W. Willems, Error probabilities for bounded distance decoding, Des. Codes Crypt., 40 (2006), 237-252.
doi: 10.1007/s10623-006-0010-x. |
[7] |
A. M. Gleason, Weight polynomials of self-dual codes and the MacWilliams identities, Actes Congrès Internat. Math., 3 (1970), 211-215. |
[8] |
F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes,'' North Holland, Amsterdam, 1977. |
[9] |
C. L. Mallows and N. J. A. Sloane, An upper bound for self-dual codes, Inform. Control, 22 (1973), 188-200.
doi: 10.1016/S0019-9958(73)90273-8. |
[10] |
E. M. Rains, Shadow bounds for self-dual-codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[11] |
E. M. Rains and N. J. A. Sloane, Self-dual codes, in "Handbook of Coding Theory'' (eds. V.S. Pless and W.C. Huffman), Elsevier, Amsterdam, (1998), 177-294. |
[12] |
V. Yorgov, On the minimal weight of some singly-even codes, IEEE Trans. Inform. Theory, 45 (1999), 2539-2541.
doi: 10.1109/18.796401. |
[13] |
S. Zhang, On the nonexistence of extremal self-dual codes, Discrete Appl. Math., 91 (1999), 277-286.
doi: 10.1016/S0166-218X(98)00131-0. |
show all references
References:
[1] |
C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows, J. Combin. Theory A, 105 (2004), 15-34.
doi: 10.1016/j.jcta.2003.09.003. |
[2] |
S. Bouyuklieva and V. Yorgov, Singly-even codes of length 40, Des. Codes Crypt., 9 (1996), 131-141.
doi: 10.1007/BF00124589. |
[3] |
Y. Cheng and N. J. A. Sloane, Codes from symmetry groups, and a $[32,17,8]$ code, SIAM J. Discrete Math., 2 (1989), 28-37.
doi: 10.1137/0402003. |
[4] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[5] |
R. Doncheva and M. Harada, Some extremal self-dual codes with an automorphism of order 7, Appl. Algebra Eng. Comm. Comp., 14 (2003), 75-79.
doi: 10.1007/s00200-003-0126-4. |
[6] |
A. Faldum, J. Lafuente, G. Ochoa and W. Willems, Error probabilities for bounded distance decoding, Des. Codes Crypt., 40 (2006), 237-252.
doi: 10.1007/s10623-006-0010-x. |
[7] |
A. M. Gleason, Weight polynomials of self-dual codes and the MacWilliams identities, Actes Congrès Internat. Math., 3 (1970), 211-215. |
[8] |
F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes,'' North Holland, Amsterdam, 1977. |
[9] |
C. L. Mallows and N. J. A. Sloane, An upper bound for self-dual codes, Inform. Control, 22 (1973), 188-200.
doi: 10.1016/S0019-9958(73)90273-8. |
[10] |
E. M. Rains, Shadow bounds for self-dual-codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[11] |
E. M. Rains and N. J. A. Sloane, Self-dual codes, in "Handbook of Coding Theory'' (eds. V.S. Pless and W.C. Huffman), Elsevier, Amsterdam, (1998), 177-294. |
[12] |
V. Yorgov, On the minimal weight of some singly-even codes, IEEE Trans. Inform. Theory, 45 (1999), 2539-2541.
doi: 10.1109/18.796401. |
[13] |
S. Zhang, On the nonexistence of extremal self-dual codes, Discrete Appl. Math., 91 (1999), 277-286.
doi: 10.1016/S0166-218X(98)00131-0. |
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