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On $q$-analogs of Steiner systems and covering designs
Large constant dimension codes and lexicodes
1. | Computer Science Department, Technion - Israel Institute of Technology, Haifa, 32000, Israel |
References:
[1] |
G. E. Andrews and K. Eriksson, "Integer Partitions,'' Cambridge University Press, 2004. |
[2] |
J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Trans. Inform. Theory, 32 (1986), 337-348.
doi: 10.1109/TIT.1986.1057187. |
[3] |
P. Delsarte, Bilinear forms over a finite field, with applications to coding theory, J. Combin. Theory Ser. A, 25 (1978), 226-241.
doi: 10.1016/0097-3165(78)90015-8. |
[4] |
T. Etzion and N. Silberstein, Error-correcting codes in projective space via rank-metric codes and Ferrers diagrams, IEEE Trans. Inform. Theory, 55 (2009), 2909-2919.
doi: 10.1109/TIT.2009.2021376. |
[5] |
T. Etzion and A. Vardy, Error-correcting codes in projective space, in "Proceedings of International Symposium on Information Theory,'' (2008), 871-875. |
[6] |
T. Etzion and A. Vardy, On $q$-analogs for Steiner systems and covering designs, Adv. Math. Commun., 5 (2011), 161-176. |
[7] |
W. Fulton, "Young Tableaux,'' Cambridge University Press, 1997. |
[8] |
E. M. Gabidulin, Theory of codes with maximal rank distance, Probl. Inform. Transm., 21 (1985), 1-12. |
[9] |
M. Gadouleau and Z. Yan, Constant-rank codes and their connection to constant-dimension codes, IEEE Trans. Inform. Theory, 56 (2010), 3207-3216.
doi: 10.1109/TIT.2010.2048447. |
[10] |
R. Koetter and F. R. Kschischang, Coding for errors and erasures in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
[11] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, Lecture Notes Comp. Sci., 5393 (2008), 31-42.
doi: 10.1007/978-3-540-89994-5_4. |
[12] |
V. L. Levenshtein, A class of systematic codes, Soviet Math. Dokl., 1 (1960), 368-371. |
[13] |
J. H. van Lint and R. M. Wilson, "A Course in Combinatorics,'' 2nd edition, Cambridge University Press, 2001. |
[14] |
R. M. Roth, Maximum-rank array codes and their application to crisscross error correction, IEEE Trans. Inform. Theory, 37 (1991), 328-336.
doi: 10.1109/18.75248. |
[15] |
N. Silberstein and T. Etzion, Enumerative coding for Grassmannian space, IEEE Trans. Inform. Theory, 57 (2011), 365-374.
doi: 10.1109/TIT.2010.2090252. |
[16] |
D. Silva, F. R. Kschischang and R. Koetter, A rank-metric approach to error control in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
[17] |
V. Skachek, Recursive code construction for random networks, IEEE Trans. Inform. Theory, 56 (2010), 1378-1382.
doi: 10.1109/TIT.2009.2039163. |
[18] |
R. P. Stanley, "Enumerative Combinatorics,'' Wadsworth, 1986. |
[19] |
A. J. Van Zanten, Lexicographic order and linearity, Des. Codes Crypt., 10 (1997), 85-97.
doi: 10.1023/A:1008244404559. |
show all references
References:
[1] |
G. E. Andrews and K. Eriksson, "Integer Partitions,'' Cambridge University Press, 2004. |
[2] |
J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Trans. Inform. Theory, 32 (1986), 337-348.
doi: 10.1109/TIT.1986.1057187. |
[3] |
P. Delsarte, Bilinear forms over a finite field, with applications to coding theory, J. Combin. Theory Ser. A, 25 (1978), 226-241.
doi: 10.1016/0097-3165(78)90015-8. |
[4] |
T. Etzion and N. Silberstein, Error-correcting codes in projective space via rank-metric codes and Ferrers diagrams, IEEE Trans. Inform. Theory, 55 (2009), 2909-2919.
doi: 10.1109/TIT.2009.2021376. |
[5] |
T. Etzion and A. Vardy, Error-correcting codes in projective space, in "Proceedings of International Symposium on Information Theory,'' (2008), 871-875. |
[6] |
T. Etzion and A. Vardy, On $q$-analogs for Steiner systems and covering designs, Adv. Math. Commun., 5 (2011), 161-176. |
[7] |
W. Fulton, "Young Tableaux,'' Cambridge University Press, 1997. |
[8] |
E. M. Gabidulin, Theory of codes with maximal rank distance, Probl. Inform. Transm., 21 (1985), 1-12. |
[9] |
M. Gadouleau and Z. Yan, Constant-rank codes and their connection to constant-dimension codes, IEEE Trans. Inform. Theory, 56 (2010), 3207-3216.
doi: 10.1109/TIT.2010.2048447. |
[10] |
R. Koetter and F. R. Kschischang, Coding for errors and erasures in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
[11] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, Lecture Notes Comp. Sci., 5393 (2008), 31-42.
doi: 10.1007/978-3-540-89994-5_4. |
[12] |
V. L. Levenshtein, A class of systematic codes, Soviet Math. Dokl., 1 (1960), 368-371. |
[13] |
J. H. van Lint and R. M. Wilson, "A Course in Combinatorics,'' 2nd edition, Cambridge University Press, 2001. |
[14] |
R. M. Roth, Maximum-rank array codes and their application to crisscross error correction, IEEE Trans. Inform. Theory, 37 (1991), 328-336.
doi: 10.1109/18.75248. |
[15] |
N. Silberstein and T. Etzion, Enumerative coding for Grassmannian space, IEEE Trans. Inform. Theory, 57 (2011), 365-374.
doi: 10.1109/TIT.2010.2090252. |
[16] |
D. Silva, F. R. Kschischang and R. Koetter, A rank-metric approach to error control in random network coding, IEEE Trans. Inform. Theory, 54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
[17] |
V. Skachek, Recursive code construction for random networks, IEEE Trans. Inform. Theory, 56 (2010), 1378-1382.
doi: 10.1109/TIT.2009.2039163. |
[18] |
R. P. Stanley, "Enumerative Combinatorics,'' Wadsworth, 1986. |
[19] |
A. J. Van Zanten, Lexicographic order and linearity, Des. Codes Crypt., 10 (1997), 85-97.
doi: 10.1023/A:1008244404559. |
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