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Cyclic orbit codes and stabilizer subfields
1. | University of Kentucky, Department of Mathematics, Lexington, KY 40506-0027 |
2. | School of Mathematical Sciences, University of Northern Colorado, Greeley, CO 80639, United States |
3. | Department of Mathematics, University of Kentucky, Lexington, KY 40506-0027, United States |
References:
[1] |
R. Ahlswede, N. Cai, S.-Y. R. Li and R. W. Yeung, Network information flow, IEEE Trans. Inf. Theory, IT-46 (2000), 1204-1216.
doi: 10.1109/18.850663. |
[2] |
M. Braun, T. Etzion, P. Östergård, A. Vardy and A. Wassermann, Existence of $q$-analogs of Steiner systems,, preprint, ().
|
[3] |
S. El-Zanati, H. Jordon, G. Seelinger, P. Sissokho and L. Spence, The maximum size of a partial $3$-spread in a finite vector space over $\mathbb F_2$, Des. Codes Crypt., 54 (2010), 101-107.
doi: 10.1007/s10623-009-9311-1. |
[4] |
A. Elsenhans, A. Kohnert and A. Wassermann, Construction of codes for network coding, in Proc. 19th Int. Symp. Math. Theory Netw. Syst., Budapest, Hungary, 2010, 1811-1814. |
[5] |
T. Etzion and N. Silberstein, Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams, IEEE Trans. Inf. Theory, IT-55 (2009), 2909-2919.
doi: 10.1109/TIT.2009.2021376. |
[6] |
T. Etzion and A. Vardy, Error-correcting codes in projective geometry, IEEE Trans. Inf. Theory, IT-57 (2011), 1165-1173.
doi: 10.1109/TIT.2010.2095232. |
[7] |
T. Etzion and A. Vardy, On $q$-analogs of Steiner systems and covering designs, Adv. Math. Commun., 5 (2011), 161-176.
doi: 10.3934/amc.2011.5.161. |
[8] |
E. M. Gabidulin, Theory of codes with maximal rank distance, Probl. Inf. Transm., 21 (1985), 1-12. |
[9] |
E. M. Gabidulin, N. I. Pilipchuk and M. Bossert, Decoding of random network codes, Probl. Inf. Trans. (Engl. Transl.), 46 (2010), 300-320.
doi: 10.1134/S0032946010040034. |
[10] |
A. Khaleghi, D. Silva and F. R. Kschischang, Subspace codes, in Proc. 12th IMA Conf. Crypt. Coding, Cirencester, 2009, 1-21.
doi: 10.1007/978-3-642-10868-6_1. |
[11] |
R. Koetter and F. R. Kschischang, Coding for errors and erasures in random network coding, IEEE Trans. Inf. Theory, IT-54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
[12] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in Mathematical Methods in Computer Science (eds. J. Calmet, W. Geiselmann and J. Müller-Quade), Springer, Berlin, 2008, 31-42.
doi: 10.1007/978-3-540-89994-5_4. |
[13] |
J. Rosenthal and A.-L. Trautmann, A complete characterization of irreducible cyclic orbit codes and their Plücker embedding, Des. Codes Crypt., 66 (2013), 275-289.
doi: 10.1007/s10623-012-9691-5. |
[14] |
D. Silva and F. R. Kschischang and R. Kötter, A rank-metric approach to error control in random network coding, IEEE Trans. Inf. Theory, IT-54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
[15] |
A.-L. Trautmann, Isometry and automorphisms of constant dimension codes, Adv. Math. Commun., 7 (2013), 147-160.
doi: 10.3934/amc.2013.7.147. |
[16] |
A.-L. Trautmann, F. Manganiello, M. Braun and J. Rosenthal, Cyclic orbit codes, IEEE Trans. Inf. Theory, IT-59 (2013), 7386-7404.
doi: 10.1109/TIT.2013.2274266. |
[17] |
S.-T. Xia and F.-W. Fu, Johnson type bounds on constant dimension codes, Des. Codes Crypt., 50 (2009), 163-172.
doi: 10.1007/s10623-008-9221-7. |
show all references
References:
[1] |
R. Ahlswede, N. Cai, S.-Y. R. Li and R. W. Yeung, Network information flow, IEEE Trans. Inf. Theory, IT-46 (2000), 1204-1216.
doi: 10.1109/18.850663. |
[2] |
M. Braun, T. Etzion, P. Östergård, A. Vardy and A. Wassermann, Existence of $q$-analogs of Steiner systems,, preprint, ().
|
[3] |
S. El-Zanati, H. Jordon, G. Seelinger, P. Sissokho and L. Spence, The maximum size of a partial $3$-spread in a finite vector space over $\mathbb F_2$, Des. Codes Crypt., 54 (2010), 101-107.
doi: 10.1007/s10623-009-9311-1. |
[4] |
A. Elsenhans, A. Kohnert and A. Wassermann, Construction of codes for network coding, in Proc. 19th Int. Symp. Math. Theory Netw. Syst., Budapest, Hungary, 2010, 1811-1814. |
[5] |
T. Etzion and N. Silberstein, Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams, IEEE Trans. Inf. Theory, IT-55 (2009), 2909-2919.
doi: 10.1109/TIT.2009.2021376. |
[6] |
T. Etzion and A. Vardy, Error-correcting codes in projective geometry, IEEE Trans. Inf. Theory, IT-57 (2011), 1165-1173.
doi: 10.1109/TIT.2010.2095232. |
[7] |
T. Etzion and A. Vardy, On $q$-analogs of Steiner systems and covering designs, Adv. Math. Commun., 5 (2011), 161-176.
doi: 10.3934/amc.2011.5.161. |
[8] |
E. M. Gabidulin, Theory of codes with maximal rank distance, Probl. Inf. Transm., 21 (1985), 1-12. |
[9] |
E. M. Gabidulin, N. I. Pilipchuk and M. Bossert, Decoding of random network codes, Probl. Inf. Trans. (Engl. Transl.), 46 (2010), 300-320.
doi: 10.1134/S0032946010040034. |
[10] |
A. Khaleghi, D. Silva and F. R. Kschischang, Subspace codes, in Proc. 12th IMA Conf. Crypt. Coding, Cirencester, 2009, 1-21.
doi: 10.1007/978-3-642-10868-6_1. |
[11] |
R. Koetter and F. R. Kschischang, Coding for errors and erasures in random network coding, IEEE Trans. Inf. Theory, IT-54 (2008), 3579-3591.
doi: 10.1109/TIT.2008.926449. |
[12] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in Mathematical Methods in Computer Science (eds. J. Calmet, W. Geiselmann and J. Müller-Quade), Springer, Berlin, 2008, 31-42.
doi: 10.1007/978-3-540-89994-5_4. |
[13] |
J. Rosenthal and A.-L. Trautmann, A complete characterization of irreducible cyclic orbit codes and their Plücker embedding, Des. Codes Crypt., 66 (2013), 275-289.
doi: 10.1007/s10623-012-9691-5. |
[14] |
D. Silva and F. R. Kschischang and R. Kötter, A rank-metric approach to error control in random network coding, IEEE Trans. Inf. Theory, IT-54 (2008), 3951-3967.
doi: 10.1109/TIT.2008.928291. |
[15] |
A.-L. Trautmann, Isometry and automorphisms of constant dimension codes, Adv. Math. Commun., 7 (2013), 147-160.
doi: 10.3934/amc.2013.7.147. |
[16] |
A.-L. Trautmann, F. Manganiello, M. Braun and J. Rosenthal, Cyclic orbit codes, IEEE Trans. Inf. Theory, IT-59 (2013), 7386-7404.
doi: 10.1109/TIT.2013.2274266. |
[17] |
S.-T. Xia and F.-W. Fu, Johnson type bounds on constant dimension codes, Des. Codes Crypt., 50 (2009), 163-172.
doi: 10.1007/s10623-008-9221-7. |
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