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Input-state-output representations and constructions of finite support 2D convolutional codes
Bounds for binary codes relative to pseudo-distances of $k$ points
1. | Université Bordeaux I, Institut de Mathématiques, 351, cours de la Libération, 33405 Talence, France, France |
References:
[1] |
A. Ashikhmin, A. Barg and S. Litsyn, New upper bounds on generalized weights,, IEEE Trans. Inform. Theory, IT-45 (1999), 1258.
doi: 10.1109/18.761280. |
[2] |
L. A. Bassalygo, Supports of a code,, in, (1995), 1. Google Scholar |
[3] |
C. Bachoc, Semidefinite programming, harmonic analysis and coding theory,, Lecture notes of a CIMPA course, (2009). Google Scholar |
[4] |
C. Bachoc, D. Gijswijt, A. Schrijver and F. Vallentin, Invariant semidefinite programs,, preprint, (). Google Scholar |
[5] |
V. M. Blinovskii, Bounds for codes in the case of list decoding of finite volume,, Problems of Information Transmission, 22 (1986), 7. Google Scholar |
[6] |
V. M. Blinovskii, Generalization of Plotkin bound to the case of multiple packing,, in, (2009). Google Scholar |
[7] |
G. Cohen, S. Litsyn and G. Zémor, Upper bounds on generalized Hamming distances,, IEEE Trans. Inform. Theory, 40 (1994), 2090.
doi: 10.1109/18.340487. |
[8] |
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups,'', Springer-Verlag, (1988).
|
[9] |
P. Delsarte, An algebraic approach to the association schemes of coding theory,, Philips Res. Rep. Suppl., (1973).
|
[10] |
P. Delsarte, Hahn polynomials, discrete harmonics and $t$-designs,, SIAM J. Appl. Math., 34 (1978), 157.
doi: 10.1137/0134012. |
[11] |
V. Guruswami, List decoding from erasures: bounds and code constructions,, IEEE Trans. Inform. Theory, IT-49 (2003), 2826.
doi: 10.1109/TIT.2003.815776. |
[12] |
V. I. Levenshtein, Universal bounds for codes and designs,, in, (1998), 499.
|
[13] |
R. J. McEliece, E. R. Rodemich, H. Rumsey and L. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities,, IEEE Trans. Inform. Theory, IT-23 (1977), 157.
doi: 10.1109/TIT.1977.1055688. |
[14] |
L. H. Ozarow and A. D. Wyner, Wire-tap channel II,, in, (1985), 33.
|
[15] |
A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming,, IEEE Trans. Inform. Theory, IT-51 (2005), 2859.
doi: 10.1109/TIT.2005.851748. |
[16] |
M. Sudan, Decoding of Reed Solomon codes beyond the error-correction bound,, Journal of Complexity, 13 (1997), 180.
doi: 10.1006/jcom.1997.0439. |
[17] |
F. Vallentin, Lecture notes: Semidefinite programs and harmonic analysis,, preprint, (). Google Scholar |
[18] |
F. Vallentin, Symmetry in semidefinite programs,, Linear Algebra and Appl., 430 (2009), 360.
doi: 10.1016/j.laa.2008.07.025. |
[19] |
V. K. Wei, Generalized Hamming weights for linear codes,, IEEE Trans. Inform. Theory, IT-37 (1991), 1412.
doi: 10.1109/18.133259. |
[20] |
G. Zémor, Threshold effects in codes,, in, (1993).
|
[21] |
G. Zémor and G. Cohen, The threshold probability of a code,, IEEE Trans. Inform. Theory, IT-41 (1995), 469.
doi: 10.1109/18.370148. |
show all references
References:
[1] |
A. Ashikhmin, A. Barg and S. Litsyn, New upper bounds on generalized weights,, IEEE Trans. Inform. Theory, IT-45 (1999), 1258.
doi: 10.1109/18.761280. |
[2] |
L. A. Bassalygo, Supports of a code,, in, (1995), 1. Google Scholar |
[3] |
C. Bachoc, Semidefinite programming, harmonic analysis and coding theory,, Lecture notes of a CIMPA course, (2009). Google Scholar |
[4] |
C. Bachoc, D. Gijswijt, A. Schrijver and F. Vallentin, Invariant semidefinite programs,, preprint, (). Google Scholar |
[5] |
V. M. Blinovskii, Bounds for codes in the case of list decoding of finite volume,, Problems of Information Transmission, 22 (1986), 7. Google Scholar |
[6] |
V. M. Blinovskii, Generalization of Plotkin bound to the case of multiple packing,, in, (2009). Google Scholar |
[7] |
G. Cohen, S. Litsyn and G. Zémor, Upper bounds on generalized Hamming distances,, IEEE Trans. Inform. Theory, 40 (1994), 2090.
doi: 10.1109/18.340487. |
[8] |
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups,'', Springer-Verlag, (1988).
|
[9] |
P. Delsarte, An algebraic approach to the association schemes of coding theory,, Philips Res. Rep. Suppl., (1973).
|
[10] |
P. Delsarte, Hahn polynomials, discrete harmonics and $t$-designs,, SIAM J. Appl. Math., 34 (1978), 157.
doi: 10.1137/0134012. |
[11] |
V. Guruswami, List decoding from erasures: bounds and code constructions,, IEEE Trans. Inform. Theory, IT-49 (2003), 2826.
doi: 10.1109/TIT.2003.815776. |
[12] |
V. I. Levenshtein, Universal bounds for codes and designs,, in, (1998), 499.
|
[13] |
R. J. McEliece, E. R. Rodemich, H. Rumsey and L. Welch, New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities,, IEEE Trans. Inform. Theory, IT-23 (1977), 157.
doi: 10.1109/TIT.1977.1055688. |
[14] |
L. H. Ozarow and A. D. Wyner, Wire-tap channel II,, in, (1985), 33.
|
[15] |
A. Schrijver, New code upper bounds from the Terwilliger algebra and semidefinite programming,, IEEE Trans. Inform. Theory, IT-51 (2005), 2859.
doi: 10.1109/TIT.2005.851748. |
[16] |
M. Sudan, Decoding of Reed Solomon codes beyond the error-correction bound,, Journal of Complexity, 13 (1997), 180.
doi: 10.1006/jcom.1997.0439. |
[17] |
F. Vallentin, Lecture notes: Semidefinite programs and harmonic analysis,, preprint, (). Google Scholar |
[18] |
F. Vallentin, Symmetry in semidefinite programs,, Linear Algebra and Appl., 430 (2009), 360.
doi: 10.1016/j.laa.2008.07.025. |
[19] |
V. K. Wei, Generalized Hamming weights for linear codes,, IEEE Trans. Inform. Theory, IT-37 (1991), 1412.
doi: 10.1109/18.133259. |
[20] |
G. Zémor, Threshold effects in codes,, in, (1993).
|
[21] |
G. Zémor and G. Cohen, The threshold probability of a code,, IEEE Trans. Inform. Theory, IT-41 (1995), 469.
doi: 10.1109/18.370148. |
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