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On the error distance of extended Reed-Solomon codes
Coherence of sensing matrices coming from algebraic-geometric codes
1. | Department of Mathematics, Sookmyung Women's University, Cheongpa-ro 47 gil 100, Yongsan-Ku, Seoul 140-742, South Korea |
References:
[1] |
P. Beelen, The order bound for general algebraic geometric codes, Finite Fields Appl., 13 (2007), 665-680.
doi: 10.1016/j.ffa.2006.09.006. |
[2] |
J. Bourgain, S. Dilworth, K. Ford, S. Konyagin and D. Kutzarova, Explicit constructions of RIP matrices and related problems, Duke Math. J., 159 (2011), 145-185.
doi: 10.1215/00127094-1384809. |
[3] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. J. Candès and T. Tao, Decoding by linear programming, IEEE Trans. Inf. Theory, 51 (2005), 4203-4215.
doi: 10.1109/TIT.2005.858979. |
[5] |
R. A. DeVore, Deterministic constructions of compressed sensing matrices, J. Complexity, 23 (2007), 918-925.
doi: 10.1016/j.jco.2007.04.002. |
[6] |
D. L. Donoho, Compressed sensing, IEEE Trans. Inf. Theory, 52 (2006), 1289-1306.
doi: 10.1109/TIT.2006.871582. |
[7] |
M. Homma and S. J. Kim, Toward the determination of the minimum distance of two-point codes on a Hermitian curve, Des. Codes Crypt., 37 (2005), 111-132.
doi: 10.1007/s10623-004-3807-5. |
[8] |
M. Homma and S. J. Kim, The complete determination of the minimum distance of two-point codes on a Hermitian curve, Des. Codes Crypt., 40 (2006), 5-24.
doi: 10.1007/s10623-005-4599-y. |
[9] |
M. Homma and S. J. Kim, The two-point codes on a Hermitian curve with the designed minimum distance, Des. Codes Crypt., 38 (2006), 55-81.
doi: 10.1007/s10623-004-5661-x. |
[10] |
M. Homma and S. J. Kim, The two-point codes with the designed distance on a Hermitian curve in even characteristic, Des. Codes Crypt., 39 (2006), 375-386.
doi: 10.1007/s10623-005-5471-9. |
[11] |
C. Kirfel and R. Pellikaan, The minimum distance of codes in an array coming from telescopic semigroups, IEEE Trans. Inf. Theory, 41 (1995), 1720-1732.
doi: 10.1109/18.476245. |
[12] |
S. Li, F. Gao, G. Ge and S. Zhang, Deterministic construction of compressed sensing matrices via algebraic curves, IEEE Trans. Inf. Theory, 58 (2012), 5035-5041.
doi: 10.1109/TIT.2012.2196256. |
[13] |
G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes, Des. Codes Crypt., 22 (2001), 107-121.
doi: 10.1023/A:1008311518095. |
[14] |
S. Park, Minimum distance of Hermitian two-point codes, Des. Codes Crypt., 57 (2010), 195-213.
doi: 10.1007/s10623-009-9361-4. |
[15] |
H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edition, Springer-Verlag, Berlin, 2009. |
[16] |
C. P. Xing and H. Chen, Improvements on parameters of one-point AG codes from Hermitian curves, IEEE Trans. Inf. Theory, 48 (2002), 535-537.
doi: 10.1109/18.979330. |
show all references
References:
[1] |
P. Beelen, The order bound for general algebraic geometric codes, Finite Fields Appl., 13 (2007), 665-680.
doi: 10.1016/j.ffa.2006.09.006. |
[2] |
J. Bourgain, S. Dilworth, K. Ford, S. Konyagin and D. Kutzarova, Explicit constructions of RIP matrices and related problems, Duke Math. J., 159 (2011), 145-185.
doi: 10.1215/00127094-1384809. |
[3] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inf. Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. J. Candès and T. Tao, Decoding by linear programming, IEEE Trans. Inf. Theory, 51 (2005), 4203-4215.
doi: 10.1109/TIT.2005.858979. |
[5] |
R. A. DeVore, Deterministic constructions of compressed sensing matrices, J. Complexity, 23 (2007), 918-925.
doi: 10.1016/j.jco.2007.04.002. |
[6] |
D. L. Donoho, Compressed sensing, IEEE Trans. Inf. Theory, 52 (2006), 1289-1306.
doi: 10.1109/TIT.2006.871582. |
[7] |
M. Homma and S. J. Kim, Toward the determination of the minimum distance of two-point codes on a Hermitian curve, Des. Codes Crypt., 37 (2005), 111-132.
doi: 10.1007/s10623-004-3807-5. |
[8] |
M. Homma and S. J. Kim, The complete determination of the minimum distance of two-point codes on a Hermitian curve, Des. Codes Crypt., 40 (2006), 5-24.
doi: 10.1007/s10623-005-4599-y. |
[9] |
M. Homma and S. J. Kim, The two-point codes on a Hermitian curve with the designed minimum distance, Des. Codes Crypt., 38 (2006), 55-81.
doi: 10.1007/s10623-004-5661-x. |
[10] |
M. Homma and S. J. Kim, The two-point codes with the designed distance on a Hermitian curve in even characteristic, Des. Codes Crypt., 39 (2006), 375-386.
doi: 10.1007/s10623-005-5471-9. |
[11] |
C. Kirfel and R. Pellikaan, The minimum distance of codes in an array coming from telescopic semigroups, IEEE Trans. Inf. Theory, 41 (1995), 1720-1732.
doi: 10.1109/18.476245. |
[12] |
S. Li, F. Gao, G. Ge and S. Zhang, Deterministic construction of compressed sensing matrices via algebraic curves, IEEE Trans. Inf. Theory, 58 (2012), 5035-5041.
doi: 10.1109/TIT.2012.2196256. |
[13] |
G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes, Des. Codes Crypt., 22 (2001), 107-121.
doi: 10.1023/A:1008311518095. |
[14] |
S. Park, Minimum distance of Hermitian two-point codes, Des. Codes Crypt., 57 (2010), 195-213.
doi: 10.1007/s10623-009-9361-4. |
[15] |
H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edition, Springer-Verlag, Berlin, 2009. |
[16] |
C. P. Xing and H. Chen, Improvements on parameters of one-point AG codes from Hermitian curves, IEEE Trans. Inf. Theory, 48 (2002), 535-537.
doi: 10.1109/18.979330. |
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