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On $q$-ary linear completely regular codes with $\rho=2$ and antipodal dual
On dual extremal maximal self-orthogonal codes of Type I-IV
1. | Lehrstuhl D für Mathematik, RWTH Aachen University, Templergraben 64, 52062 Aachen, Germany |
References:
[1] |
C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows, J. Combin. Theory, 105 (2004), 15-34.
doi: 10.1016/j.jcta.2003.09.003. |
[2] |
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. |
[3] |
P. Gaborit, A bound for certain s-extremal lattices and codes, Arch. Math. (Basel), 89 (2007), 143-151. |
[4] |
A. M. Gleason, Weight polynomials of self-dual codes and the MacWilliams identites, in "Actes, Congr. Int. Math.'' (ed. P. Gauthier-Villars), 3 (1971), 211-215. |
[5] |
W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes," Cambridge University Press, Cambridge, 2003. |
[6] |
G. Nebe, E. M. Rains and N. J. A. Sloane, "Self-Dual Codes and Invariant Theory," Springer, Berlin, 2006. |
[7] |
M. Ozeki, On intersection properties of extremal ternary codes, J. Math. Industry, 1 (2009), 105-121. |
[8] |
V. Pless, W. C. Huffman and R. A. Brualdi (eds.), "Handbook of Coding Theory," North-Holland, Amsterdam, 1998. |
[9] |
V. Pless, N. J. A. Sloane and H. N. Ward, Ternary codes of minimum weight 6, and the classification of length 20, IEEE Trans. Inform. Theory, 26 (1980), 305-316.
doi: 10.1109/TIT.1980.1056195. |
[10] |
E. M. Rains, Shadow bounds for self-dual codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[11] |
W. Scharlau, Quadratic and Hermitian forms, in "Grundlehren der Mathematischen Wissenschaften," Springer-Verlag, 1985. |
[12] |
N. J. A. Sloane, Gleason's Theorem on self-dual codes and its generalizations,, preprint, ().
|
show all references
References:
[1] |
C. Bachoc and P. Gaborit, Designs and self-dual codes with long shadows, J. Combin. Theory, 105 (2004), 15-34.
doi: 10.1016/j.jcta.2003.09.003. |
[2] |
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. |
[3] |
P. Gaborit, A bound for certain s-extremal lattices and codes, Arch. Math. (Basel), 89 (2007), 143-151. |
[4] |
A. M. Gleason, Weight polynomials of self-dual codes and the MacWilliams identites, in "Actes, Congr. Int. Math.'' (ed. P. Gauthier-Villars), 3 (1971), 211-215. |
[5] |
W. C. Huffman and V. Pless, "Fundamentals of Error-Correcting Codes," Cambridge University Press, Cambridge, 2003. |
[6] |
G. Nebe, E. M. Rains and N. J. A. Sloane, "Self-Dual Codes and Invariant Theory," Springer, Berlin, 2006. |
[7] |
M. Ozeki, On intersection properties of extremal ternary codes, J. Math. Industry, 1 (2009), 105-121. |
[8] |
V. Pless, W. C. Huffman and R. A. Brualdi (eds.), "Handbook of Coding Theory," North-Holland, Amsterdam, 1998. |
[9] |
V. Pless, N. J. A. Sloane and H. N. Ward, Ternary codes of minimum weight 6, and the classification of length 20, IEEE Trans. Inform. Theory, 26 (1980), 305-316.
doi: 10.1109/TIT.1980.1056195. |
[10] |
E. M. Rains, Shadow bounds for self-dual codes, IEEE Trans. Inform. Theory, 44 (1998), 134-139.
doi: 10.1109/18.651000. |
[11] |
W. Scharlau, Quadratic and Hermitian forms, in "Grundlehren der Mathematischen Wissenschaften," Springer-Verlag, 1985. |
[12] |
N. J. A. Sloane, Gleason's Theorem on self-dual codes and its generalizations,, preprint, ().
|
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