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Syndrome decoding for Hermite codes with a Sugiyama-type algorithm
An algebraic approach for decoding spread codes
1. | Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, 2000 Neuchâtel, Switzerland |
2. | Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, M5S 3G4, Canada |
3. | Institut für Mathematik, Universität Zürich, 8057 Zürich, 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] |
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. |
[3] |
T. Etzion and A. Vardy, Error-correcting codes in projective space, in "IEEE International Symposium on Information Theory,'' (2008), 871-875. |
[4] |
È. M. Gabidulin, Theory of codes with maximum rank distance, Problemy Peredachi Informatsii, 21 (1985), 3-16. |
[5] |
E. Gorla, C. Puttmann and J. Shokrollahi, Explicit formulas for efficient multiplication in $GF(3$6m$)$, in "Selected Areas in Cryptography: Revised Selected Papers from the 14th International Workshop (SAC 2007) held at University of Ottawa'' (eds. C. Adams, A. Miri and M. Wiener), Springer, (2007), 173-183. |
[6] |
J. W. P. Hirschfeld, "Projective Geometries over Finite Fields,'' 2nd edition, The Clarendon Press, Oxford University Press, New York, 1998. |
[7] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in "MMICS'' (eds. J. Calmet, W. Geiselmann and J. Müller-Quade), Springer, (2008), 31-42. |
[8] |
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. |
[9] |
S.-Y. R. Li, R. W. Yeung and N. Cai, Linear network coding, IEEE Trans. Inform. Theory, 49 (2003), 371-381.
doi: 10.1109/TIT.2002.807285. |
[10] |
R. Lidl and H. Niederreiter, "Introduction to Finite Fields and their Applications,'' revised edition, Cambridge University Press, Cambridge, 1994.
doi: 10.1017/CBO9781139172769. |
[11] |
P. Loidreau, A Welch-Berlekamp like algorithm for decoding Gabidulin codes, in "Coding and Cryptography,'' Springer, Berlin, (2006), 36-45.
doi: 10.1007/11779360_4. |
[12] |
H. Mahdavifar and A. Vardy, Algebraic list-decoding on the operator channel, in "Proceedings of 2010 IEEE International Symposium on Information Theory,'' (2010), 1193-1197.
doi: 10.1109/ISIT.2010.5513656. |
[13] |
F. Manganiello, E. Gorla and J. Rosenthal, Spread codes and spread decoding in network coding, in "Proceedings of 2008 IEEE International Symposium on Information Theory,'' Toronto, Canada, (2008), 851-855.
doi: 10.1109/ISIT.2008.4595113. |
[14] |
G. Richter and S. Plass, Fast decoding of rank-codes with rank errors and column erasures, in "Proceedings of 2008 IEEE International Symposium on Information Theory,'' (2004), page 398. |
[15] |
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. |
[16] |
V. Skachek, Recursive code construction for random networks, IEEE Trans. Inform. Theory, 56 (2010), 1378-1382.
doi: 10.1109/TIT.2009.2039163. |
[17] |
A.-L. Trautmann, F. Manganiello and J. Rosenthal, Orbit codes - a new concept in the area of network coding, in "2010 IEEE Information Theory Workshop (ITW),'' Dublin, Ireland, (2010), 1-4.
doi: 10.1109/CIG.2010.5592788. |
[18] |
A.-L. Trautmann and J. Rosenthal, A complete characterization of irreducible cyclic orbit codes, in "Proceedings of the Seventh International Workshop on Coding and Cryptography (WCC),'' (2011), 219-223. |
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] |
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. |
[3] |
T. Etzion and A. Vardy, Error-correcting codes in projective space, in "IEEE International Symposium on Information Theory,'' (2008), 871-875. |
[4] |
È. M. Gabidulin, Theory of codes with maximum rank distance, Problemy Peredachi Informatsii, 21 (1985), 3-16. |
[5] |
E. Gorla, C. Puttmann and J. Shokrollahi, Explicit formulas for efficient multiplication in $GF(3$6m$)$, in "Selected Areas in Cryptography: Revised Selected Papers from the 14th International Workshop (SAC 2007) held at University of Ottawa'' (eds. C. Adams, A. Miri and M. Wiener), Springer, (2007), 173-183. |
[6] |
J. W. P. Hirschfeld, "Projective Geometries over Finite Fields,'' 2nd edition, The Clarendon Press, Oxford University Press, New York, 1998. |
[7] |
A. Kohnert and S. Kurz, Construction of large constant dimension codes with a prescribed minimum distance, in "MMICS'' (eds. J. Calmet, W. Geiselmann and J. Müller-Quade), Springer, (2008), 31-42. |
[8] |
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. |
[9] |
S.-Y. R. Li, R. W. Yeung and N. Cai, Linear network coding, IEEE Trans. Inform. Theory, 49 (2003), 371-381.
doi: 10.1109/TIT.2002.807285. |
[10] |
R. Lidl and H. Niederreiter, "Introduction to Finite Fields and their Applications,'' revised edition, Cambridge University Press, Cambridge, 1994.
doi: 10.1017/CBO9781139172769. |
[11] |
P. Loidreau, A Welch-Berlekamp like algorithm for decoding Gabidulin codes, in "Coding and Cryptography,'' Springer, Berlin, (2006), 36-45.
doi: 10.1007/11779360_4. |
[12] |
H. Mahdavifar and A. Vardy, Algebraic list-decoding on the operator channel, in "Proceedings of 2010 IEEE International Symposium on Information Theory,'' (2010), 1193-1197.
doi: 10.1109/ISIT.2010.5513656. |
[13] |
F. Manganiello, E. Gorla and J. Rosenthal, Spread codes and spread decoding in network coding, in "Proceedings of 2008 IEEE International Symposium on Information Theory,'' Toronto, Canada, (2008), 851-855.
doi: 10.1109/ISIT.2008.4595113. |
[14] |
G. Richter and S. Plass, Fast decoding of rank-codes with rank errors and column erasures, in "Proceedings of 2008 IEEE International Symposium on Information Theory,'' (2004), page 398. |
[15] |
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. |
[16] |
V. Skachek, Recursive code construction for random networks, IEEE Trans. Inform. Theory, 56 (2010), 1378-1382.
doi: 10.1109/TIT.2009.2039163. |
[17] |
A.-L. Trautmann, F. Manganiello and J. Rosenthal, Orbit codes - a new concept in the area of network coding, in "2010 IEEE Information Theory Workshop (ITW),'' Dublin, Ireland, (2010), 1-4.
doi: 10.1109/CIG.2010.5592788. |
[18] |
A.-L. Trautmann and J. Rosenthal, A complete characterization of irreducible cyclic orbit codes, in "Proceedings of the Seventh International Workshop on Coding and Cryptography (WCC),'' (2011), 219-223. |
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