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Isometry and automorphisms of constant dimension codes
1. | Institute of Mathematics, University of Zurich, Switzerland |
References:
[1] |
R. Ahlswede, N. Cai, S.-Y. R. Li and R. W. Yeung, Network information flow, IEEE Trans. Inform. Theory, 46 (2000), 1204-1216.
doi: 10.1109/18.850663. |
[2] |
E. Artin, Geometric algebra, in "Interscience Tracts in Pure and Applied Mathematics,'' John Wiley & Sons, 1988. |
[3] |
R. Baer, Linear algebra and projective geometry, in "Pure and Applied Mathematics,'' Academic Press, 1952. |
[4] |
T. P. Berger, Isometries for rank distance and permutation group of gabidulin codes, IEEE Trans. Inform. Theory, 49 (2003), 3016-3019.
doi: 10.1109/TIT.2003.819322. |
[5] |
T. Etzion and N. Silberstein, Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams, IEEE Trans. Inform. Theory, 55 (2009), 2909-2919.
doi: 10.1109/TIT.2009.2021376. |
[6] |
T. Etzion and A. Vardy, Error-correcting codes in projective space, in "IEEE International Symposium on Information Theory,'' (2008), 871-875. |
[7] |
T. Feulner, Canonical forms and automorphisms in the projective space, preprint, 2012. |
[8] |
E. M. Gabidulin, Theory of codes with maximum rank distance, Problemy Peredachi Informatsii, 21 (1985), 3-16. |
[9] |
E. Gorla, F. Manganiello and J. Rosenthal, An algebraic approach for decoding spread codes, Adv. Math. Commun., 6 (2012), 443-466.
doi: 10.3934/amc.2012.6.443. |
[10] |
J. W. P. Hirschfeld, "Finite Projective Spaces of Three Dimensions,'' The Clarendon Press, Oxford University Press, New York, 1985. |
[11] |
J. W. P. Hirschfeld, "Projective Geometries over Finite Fields,'' 2nd edition, The Clarendon Press, Oxford University Press, New York, 1998. |
[12] |
J. W. P. Hirschfeld and J. A. Thas, "General Galois Geometries,'' The Clarendon Press, Oxford University Press, New York, 1991. |
[13] |
A. Khaleghi, D. Silva and F. R. Kschischang, Subspace codes, in "IMA Int. Conf.,'' (2009), 1-21. |
[14] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in "Mathematical Methods in Computer Science,'' Springer, Berlin, (2008), 31-42.
doi: 10.1007/978-3-540-89994-5_4. |
[15] |
R. Kötter 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. |
[16] |
F. Manganiello, E. Gorla and J. Rosenthal, Spread codes and spread decoding in network coding, in "Proceedings of the 2008 IEEE International Symposium on Information Theory,'' Toronto, (2008), 851-855.
doi: 10.1109/ISIT.2008.4595113. |
[17] |
F. Manganiello and A.-L. Trautmann, Spread decoding in extension fields, preprint, arXiv:1108.5881 |
[18] |
D. Silva and F. R. Kschischang, On metrics for error correction in network coding, IEEE Trans. Inform. Theory, 55 (2009), 5479-5490.
doi: 10.1109/TIT.2009.2032817. |
[19] |
D. Silva, F. R. Kschischang and R. Kötter, 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. |
[20] |
V. Skachek, Recursive code construction for random networks, IEEE Trans. Inform. Theory, 56 (2010), 1378-1382.
doi: 10.1109/TIT.2009.2039163. |
[21] |
A.-L. Trautmann, F. Manganiello, M. Braun and J. Rosenthal, Cyclic orbit codes, preprint, arXiv:1112.1238 |
[22] |
A.-L. Trautmann, F. Manganiello and J. Rosenthal, Orbit codes - a new concept in the area of network coding, in "IEEE Information Theory Workshop (ITW),'' Dublin, (2010), 1-4. |
show all references
References:
[1] |
R. Ahlswede, N. Cai, S.-Y. R. Li and R. W. Yeung, Network information flow, IEEE Trans. Inform. Theory, 46 (2000), 1204-1216.
doi: 10.1109/18.850663. |
[2] |
E. Artin, Geometric algebra, in "Interscience Tracts in Pure and Applied Mathematics,'' John Wiley & Sons, 1988. |
[3] |
R. Baer, Linear algebra and projective geometry, in "Pure and Applied Mathematics,'' Academic Press, 1952. |
[4] |
T. P. Berger, Isometries for rank distance and permutation group of gabidulin codes, IEEE Trans. Inform. Theory, 49 (2003), 3016-3019.
doi: 10.1109/TIT.2003.819322. |
[5] |
T. Etzion and N. Silberstein, Error-correcting codes in projective spaces via rank-metric codes and Ferrers diagrams, IEEE Trans. Inform. Theory, 55 (2009), 2909-2919.
doi: 10.1109/TIT.2009.2021376. |
[6] |
T. Etzion and A. Vardy, Error-correcting codes in projective space, in "IEEE International Symposium on Information Theory,'' (2008), 871-875. |
[7] |
T. Feulner, Canonical forms and automorphisms in the projective space, preprint, 2012. |
[8] |
E. M. Gabidulin, Theory of codes with maximum rank distance, Problemy Peredachi Informatsii, 21 (1985), 3-16. |
[9] |
E. Gorla, F. Manganiello and J. Rosenthal, An algebraic approach for decoding spread codes, Adv. Math. Commun., 6 (2012), 443-466.
doi: 10.3934/amc.2012.6.443. |
[10] |
J. W. P. Hirschfeld, "Finite Projective Spaces of Three Dimensions,'' The Clarendon Press, Oxford University Press, New York, 1985. |
[11] |
J. W. P. Hirschfeld, "Projective Geometries over Finite Fields,'' 2nd edition, The Clarendon Press, Oxford University Press, New York, 1998. |
[12] |
J. W. P. Hirschfeld and J. A. Thas, "General Galois Geometries,'' The Clarendon Press, Oxford University Press, New York, 1991. |
[13] |
A. Khaleghi, D. Silva and F. R. Kschischang, Subspace codes, in "IMA Int. Conf.,'' (2009), 1-21. |
[14] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in "Mathematical Methods in Computer Science,'' Springer, Berlin, (2008), 31-42.
doi: 10.1007/978-3-540-89994-5_4. |
[15] |
R. Kötter 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. |
[16] |
F. Manganiello, E. Gorla and J. Rosenthal, Spread codes and spread decoding in network coding, in "Proceedings of the 2008 IEEE International Symposium on Information Theory,'' Toronto, (2008), 851-855.
doi: 10.1109/ISIT.2008.4595113. |
[17] |
F. Manganiello and A.-L. Trautmann, Spread decoding in extension fields, preprint, arXiv:1108.5881 |
[18] |
D. Silva and F. R. Kschischang, On metrics for error correction in network coding, IEEE Trans. Inform. Theory, 55 (2009), 5479-5490.
doi: 10.1109/TIT.2009.2032817. |
[19] |
D. Silva, F. R. Kschischang and R. Kötter, 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. |
[20] |
V. Skachek, Recursive code construction for random networks, IEEE Trans. Inform. Theory, 56 (2010), 1378-1382.
doi: 10.1109/TIT.2009.2039163. |
[21] |
A.-L. Trautmann, F. Manganiello, M. Braun and J. Rosenthal, Cyclic orbit codes, preprint, arXiv:1112.1238 |
[22] |
A.-L. Trautmann, F. Manganiello and J. Rosenthal, Orbit codes - a new concept in the area of network coding, in "IEEE Information Theory Workshop (ITW),'' Dublin, (2010), 1-4. |
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