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Self-orthogonal codes from the strongly regular graphs on up to 40 vertices
There is no $[24,12,9]$ doubly-even self-dual code over $\mathbb F_4$
1. | Department of EE-Systems, Tel Aviv University, Tel Aviv, Israel |
2. | Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen |
References:
[1] |
E. F. Assmus, Jr. and H. F. Mattson, Jr., New $5$-designs, J. Combin. Theory, 6 (1969), 122-151. |
[2] |
K. Betsumiya, On the classification of type II codes over $\mathbbF_{2^r}$ with binary length 32, preprint. |
[3] |
K. Betsumiya, T. A. Gulliver, M. Harada and A. Munemasa, On type II codes over $\mathbbF_4$, IEEE Trans. Inform. Theory, 47 (2001), 2242-2248.
doi: 10.1109/18.945245. |
[4] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[5] |
T. Feulner, The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes, Adv. Math. Commun., 3 (2009), 363-383.
doi: 10.3934/amc.2009.3.363. |
[6] |
P. Gaborit, V. Pless, P. Solé and O. Atkin, Type II codes over $\mathbbF_4$, Finite Fields Appl., 8 (2002), 171-183.
doi: 10.1006/ffta.2001.0333. |
[7] |
A. Günther, Codes und Invariantentheorie (in German), Diploma thesis, RWTH Aachen, 2006. Available online at http://www.math.rwth-aachen.de/~Gabriele.Nebe/dipl/guenther.pdf |
[8] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.
doi: 10.1017/CBO9780511807077. |
[9] |
G. Nebe, H.-G. Quebbemann, E. M. Rains and N. J. A. Sloane, Complete weight enumerators of generalized doubly-even self-dual codes, Finite Fields Appl., 10 (2004), 540-550.
doi: 10.1016/j.ffa.2003.12.001. |
[10] |
H.-G. Quebbemann, On even codes, Discrete Math., 98 (1991), 29-34.
doi: 10.1016/0012-365X(91)90410-4. |
[11] |
The Sage Development Team, Sage Mathematics Software, Version 6.4.1, http://www.sagemath.org |
show all references
References:
[1] |
E. F. Assmus, Jr. and H. F. Mattson, Jr., New $5$-designs, J. Combin. Theory, 6 (1969), 122-151. |
[2] |
K. Betsumiya, On the classification of type II codes over $\mathbbF_{2^r}$ with binary length 32, preprint. |
[3] |
K. Betsumiya, T. A. Gulliver, M. Harada and A. Munemasa, On type II codes over $\mathbbF_4$, IEEE Trans. Inform. Theory, 47 (2001), 2242-2248.
doi: 10.1109/18.945245. |
[4] |
W. Bosma, J. Cannon and C. Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput., 24 (1997), 235-265.
doi: 10.1006/jsco.1996.0125. |
[5] |
T. Feulner, The automorphism groups of linear codes and canonical representatives of their semilinear isometry classes, Adv. Math. Commun., 3 (2009), 363-383.
doi: 10.3934/amc.2009.3.363. |
[6] |
P. Gaborit, V. Pless, P. Solé and O. Atkin, Type II codes over $\mathbbF_4$, Finite Fields Appl., 8 (2002), 171-183.
doi: 10.1006/ffta.2001.0333. |
[7] |
A. Günther, Codes und Invariantentheorie (in German), Diploma thesis, RWTH Aachen, 2006. Available online at http://www.math.rwth-aachen.de/~Gabriele.Nebe/dipl/guenther.pdf |
[8] |
W. C. Huffman and V. Pless, Fundamentals of Error-Correcting Codes, Cambridge University Press, 2003.
doi: 10.1017/CBO9780511807077. |
[9] |
G. Nebe, H.-G. Quebbemann, E. M. Rains and N. J. A. Sloane, Complete weight enumerators of generalized doubly-even self-dual codes, Finite Fields Appl., 10 (2004), 540-550.
doi: 10.1016/j.ffa.2003.12.001. |
[10] |
H.-G. Quebbemann, On even codes, Discrete Math., 98 (1991), 29-34.
doi: 10.1016/0012-365X(91)90410-4. |
[11] |
The Sage Development Team, Sage Mathematics Software, Version 6.4.1, http://www.sagemath.org |
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