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The weight distribution of the self-dual $[128,64]$ polarity design code
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On self-dual MRD codes
1. | Lehrstuhl D für Mathematik, RWTH Aachen University, 52056 Aachen |
2. | Fakultät für Mathematik, Otto-von-Guericke Universität, Magdeburg, Germany |
References:
[1] |
T. Berger, Isometries for rank distance and permutation group of Gabidulin codes, in Proc. ACCT'8, St Petersbourg, 2002, 30-33.
doi: 10.1109/TIT.2003.819322. |
[2] |
P. Delsarte, Bilinear forms over a finite field with applications to coding theory, J. Comb. Theory A, 25 (1978), 226-241.
doi: 10.1016/0097-3165(78)90015-8. |
[3] |
E. Gabidulin, Theory of codes with maximum rank distance, Probl. Inf. Transm., 21 (1985), 1-12. |
[4] | |
[5] |
A. Lempel and G. Seroussi, Factorization of symmetric matrices and trace-orthogonal bases in finite fields, SIAM J. Comput., 9 (1980), 758-767.
doi: 10.1137/0209059. |
[6] |
R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications, Cambridge Univ. Press, 1994.
doi: 10.1017/CBO9781139172769. |
[7] |
K. Morrison, Equivalence for rank-metric and matrix codes and automorphism groups of Gabidulin codes, IEEE Trans. Inform. Theory, 60 (2014), 7035-7046.
doi: 10.1109/TIT.2014.2359198. |
[8] |
K. Morrison, An enumeration of the equivalence classes of self-dual matrix codes, Adv. Math. Commun., 9 (2015), 415-436.
doi: 10.3934/amc.2015.9.415. |
[9] |
A. Ravagnani, Rank-metric codes and their duality theory, Des. Codes Cryptogr., 80 (2016), 197-216.
doi: 10.1007/s10623-015-0077-3. |
[10] |
W. Scharlau, Quadratic and Hermitian Forms, Grundlehren der mathematischen Wissenschaften 270, Springer-Verlag, Berlin, 1985.
doi: 10.1007/978-3-642-69971-9. |
[11] |
J. Sheekey, A new family of linear maximum rank distance codes, preprint, arXiv:1504.01581 |
[12] |
Z.-X. Wan, Geometry of Matrices, World Scientific, Singapore, 1996.
doi: 10.1142/9789812830234. |
show all references
References:
[1] |
T. Berger, Isometries for rank distance and permutation group of Gabidulin codes, in Proc. ACCT'8, St Petersbourg, 2002, 30-33.
doi: 10.1109/TIT.2003.819322. |
[2] |
P. Delsarte, Bilinear forms over a finite field with applications to coding theory, J. Comb. Theory A, 25 (1978), 226-241.
doi: 10.1016/0097-3165(78)90015-8. |
[3] |
E. Gabidulin, Theory of codes with maximum rank distance, Probl. Inf. Transm., 21 (1985), 1-12. |
[4] | |
[5] |
A. Lempel and G. Seroussi, Factorization of symmetric matrices and trace-orthogonal bases in finite fields, SIAM J. Comput., 9 (1980), 758-767.
doi: 10.1137/0209059. |
[6] |
R. Lidl and H. Niederreiter, Introduction to Finite Fields and their Applications, Cambridge Univ. Press, 1994.
doi: 10.1017/CBO9781139172769. |
[7] |
K. Morrison, Equivalence for rank-metric and matrix codes and automorphism groups of Gabidulin codes, IEEE Trans. Inform. Theory, 60 (2014), 7035-7046.
doi: 10.1109/TIT.2014.2359198. |
[8] |
K. Morrison, An enumeration of the equivalence classes of self-dual matrix codes, Adv. Math. Commun., 9 (2015), 415-436.
doi: 10.3934/amc.2015.9.415. |
[9] |
A. Ravagnani, Rank-metric codes and their duality theory, Des. Codes Cryptogr., 80 (2016), 197-216.
doi: 10.1007/s10623-015-0077-3. |
[10] |
W. Scharlau, Quadratic and Hermitian Forms, Grundlehren der mathematischen Wissenschaften 270, Springer-Verlag, Berlin, 1985.
doi: 10.1007/978-3-642-69971-9. |
[11] |
J. Sheekey, A new family of linear maximum rank distance codes, preprint, arXiv:1504.01581 |
[12] |
Z.-X. Wan, Geometry of Matrices, World Scientific, Singapore, 1996.
doi: 10.1142/9789812830234. |
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