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Decoding of differential AG codes
1. | Department of Mathematics Education, Chosun University, Gwangju 61452, South Korea |
References:
[1] |
P. Beelen and T. Høholdt, The decoding of algebraic geometry codes, in Advances in Algebraic Geometry Codes, World Sci. Publ., 2008, 49-98.
doi: 10.1142/9789812794017_0002. |
[2] |
I. M. Duursma, Majority coset decoding, IEEE Trans. Inf. Theory, 39 (1993), 1067-1070.
doi: 10.1109/18.256518. |
[3] |
G. L. Feng and T. T. N. Rao, Decoding algebraic-geometric codes up to the designed minimum distance, IEEE Trans. Inf. Theory, 39 (1993), 37-45.
doi: 10.1109/18.179340. |
[4] |
O. Geil, R. Matsumoto and D. Ruano, List decoding algorithms based on Gröbner bases for general one-point AG codes, in Proc. IEEE Int. Symp. Inf. Theory, 2012, 86-90. |
[5] |
O. Geil, R. Matsumoto and D. Ruano, Feng-Rao decoding of primary codes, Finite Fields Appl., 23 (2013), 35-52.
doi: 10.1016/j.ffa.2013.03.005. |
[6] |
O. Geil, C. Munuera, D. Ruano and F. Torres, On the order bounds for one-point AG codes, Adv. Math. Commun., 5 (2011), 489-504.
doi: 10.3934/amc.2011.5.489. |
[7] |
V. D. Goppa, Codes on algebraic curves, Sov. Math. Dokl., 24 (1981), 170-172. |
[8] |
T. Høholdt, J. H. van Lint and R. Pellikaan, Algebraic geometry of codes, in Handbook of Coding Theory, North-Holland, 1998, 871-961. |
[9] |
K. Lee, Bounds for generalized Hamming weights of general AG codes, Finite Fields Appl., 34 (2015), 265-279.
doi: 10.1016/j.ffa.2015.02.006. |
[10] |
K. Lee, M. Bras-Amorós and M. E. O'Sullivan, Unique decoding of general AG codes, IEEE Trans. Inf. Theory, 60 (2014), 2038-2053.
doi: 10.1109/TIT.2014.2306816. |
[11] |
S. Sakata, H. E. Jensen and T. Høholdt, Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound, IEEE Trans. Inf. Theory, 41 (1995), 1762-1768.
doi: 10.1109/18.476248. |
[12] |
H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edition, Springer-Verlag, 2009. |
show all references
References:
[1] |
P. Beelen and T. Høholdt, The decoding of algebraic geometry codes, in Advances in Algebraic Geometry Codes, World Sci. Publ., 2008, 49-98.
doi: 10.1142/9789812794017_0002. |
[2] |
I. M. Duursma, Majority coset decoding, IEEE Trans. Inf. Theory, 39 (1993), 1067-1070.
doi: 10.1109/18.256518. |
[3] |
G. L. Feng and T. T. N. Rao, Decoding algebraic-geometric codes up to the designed minimum distance, IEEE Trans. Inf. Theory, 39 (1993), 37-45.
doi: 10.1109/18.179340. |
[4] |
O. Geil, R. Matsumoto and D. Ruano, List decoding algorithms based on Gröbner bases for general one-point AG codes, in Proc. IEEE Int. Symp. Inf. Theory, 2012, 86-90. |
[5] |
O. Geil, R. Matsumoto and D. Ruano, Feng-Rao decoding of primary codes, Finite Fields Appl., 23 (2013), 35-52.
doi: 10.1016/j.ffa.2013.03.005. |
[6] |
O. Geil, C. Munuera, D. Ruano and F. Torres, On the order bounds for one-point AG codes, Adv. Math. Commun., 5 (2011), 489-504.
doi: 10.3934/amc.2011.5.489. |
[7] |
V. D. Goppa, Codes on algebraic curves, Sov. Math. Dokl., 24 (1981), 170-172. |
[8] |
T. Høholdt, J. H. van Lint and R. Pellikaan, Algebraic geometry of codes, in Handbook of Coding Theory, North-Holland, 1998, 871-961. |
[9] |
K. Lee, Bounds for generalized Hamming weights of general AG codes, Finite Fields Appl., 34 (2015), 265-279.
doi: 10.1016/j.ffa.2015.02.006. |
[10] |
K. Lee, M. Bras-Amorós and M. E. O'Sullivan, Unique decoding of general AG codes, IEEE Trans. Inf. Theory, 60 (2014), 2038-2053.
doi: 10.1109/TIT.2014.2306816. |
[11] |
S. Sakata, H. E. Jensen and T. Høholdt, Generalized Berlekamp-Massey decoding of algebraic-geometric codes up to half the Feng-Rao bound, IEEE Trans. Inf. Theory, 41 (1995), 1762-1768.
doi: 10.1109/18.476248. |
[12] |
H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edition, Springer-Verlag, 2009. |
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