-
Previous Article
A class of $p$-ary cyclic codes and their weight enumerators
- AMC Home
- This Issue
-
Next Article
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.
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.
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.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. J. Candès and T. Tao, Decoding by linear programming,, IEEE Trans. Inf. Theory, 51 (2005), 4203.
doi: 10.1109/TIT.2005.858979. |
[5] |
R. A. DeVore, Deterministic constructions of compressed sensing matrices,, J. Complexity, 23 (2007), 918.
doi: 10.1016/j.jco.2007.04.002. |
[6] |
D. L. Donoho, Compressed sensing,, IEEE Trans. Inf. Theory, 52 (2006), 1289.
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.
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.
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.
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.
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.
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.
doi: 10.1109/TIT.2012.2196256. |
[13] |
G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes,, Des. Codes Crypt., 22 (2001), 107.
doi: 10.1023/A:1008311518095. |
[14] |
S. Park, Minimum distance of Hermitian two-point codes,, Des. Codes Crypt., 57 (2010), 195.
doi: 10.1007/s10623-009-9361-4. |
[15] |
H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edition,, Springer-Verlag, (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.
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.
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.
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.
doi: 10.1109/TIT.2005.862083. |
[4] |
E. J. Candès and T. Tao, Decoding by linear programming,, IEEE Trans. Inf. Theory, 51 (2005), 4203.
doi: 10.1109/TIT.2005.858979. |
[5] |
R. A. DeVore, Deterministic constructions of compressed sensing matrices,, J. Complexity, 23 (2007), 918.
doi: 10.1016/j.jco.2007.04.002. |
[6] |
D. L. Donoho, Compressed sensing,, IEEE Trans. Inf. Theory, 52 (2006), 1289.
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.
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.
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.
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.
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.
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.
doi: 10.1109/TIT.2012.2196256. |
[13] |
G. L. Matthews, Weierstrass pairs and minimum distance of Goppa codes,, Des. Codes Crypt., 22 (2001), 107.
doi: 10.1023/A:1008311518095. |
[14] |
S. Park, Minimum distance of Hermitian two-point codes,, Des. Codes Crypt., 57 (2010), 195.
doi: 10.1007/s10623-009-9361-4. |
[15] |
H. Stichtenoth, Algebraic Function Fields and Codes, 2nd edition,, Springer-Verlag, (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.
doi: 10.1109/18.979330. |
[1] |
Steven L. Brunton, Joshua L. Proctor, Jonathan H. Tu, J. Nathan Kutz. Compressed sensing and dynamic mode decomposition. Journal of Computational Dynamics, 2015, 2 (2) : 165-191. doi: 10.3934/jcd.2015002 |
[2] |
Michael Kiermaier, Johannes Zwanzger. A $\mathbb Z$4-linear code of high minimum Lee distance derived from a hyperoval. Advances in Mathematics of Communications, 2011, 5 (2) : 275-286. doi: 10.3934/amc.2011.5.275 |
[3] |
Ying Zhang, Ling Ma, Zheng-Hai Huang. On phaseless compressed sensing with partially known support. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-8. doi: 10.3934/jimo.2019014 |
[4] |
Laura Luzzi, Ghaya Rekaya-Ben Othman, Jean-Claude Belfiore. Algebraic reduction for the Golden Code. Advances in Mathematics of Communications, 2012, 6 (1) : 1-26. doi: 10.3934/amc.2012.6.1 |
[5] |
San Ling, Buket Özkaya. New bounds on the minimum distance of cyclic codes. Advances in Mathematics of Communications, 2019, 0 (0) : 0-0. doi: 10.3934/amc.2020038 |
[6] |
Yingying Li, Stanley Osher. Coordinate descent optimization for l1 minimization with application to compressed sensing; a greedy algorithm. Inverse Problems & Imaging, 2009, 3 (3) : 487-503. doi: 10.3934/ipi.2009.3.487 |
[7] |
Song Li, Junhong Lin. Compressed sensing with coherent tight frames via $l_q$-minimization for $0 < q \leq 1$. Inverse Problems & Imaging, 2014, 8 (3) : 761-777. doi: 10.3934/ipi.2014.8.761 |
[8] |
Carlos Munuera, Fernando Torres. A note on the order bound on the minimum distance of AG codes and acute semigroups. Advances in Mathematics of Communications, 2008, 2 (2) : 175-181. doi: 10.3934/amc.2008.2.175 |
[9] |
Bram van Asch, Frans Martens. A note on the minimum Lee distance of certain self-dual modular codes. Advances in Mathematics of Communications, 2012, 6 (1) : 65-68. doi: 10.3934/amc.2012.6.65 |
[10] |
José Joaquín Bernal, Diana H. Bueno-Carreño, Juan Jacobo Simón. Cyclic and BCH codes whose minimum distance equals their maximum BCH bound. Advances in Mathematics of Communications, 2016, 10 (2) : 459-474. doi: 10.3934/amc.2016018 |
[11] |
Bernard Bonnard, Monique Chyba, Alain Jacquemard, John Marriott. Algebraic geometric classification of the singular flow in the contrast imaging problem in nuclear magnetic resonance. Mathematical Control & Related Fields, 2013, 3 (4) : 397-432. doi: 10.3934/mcrf.2013.3.397 |
[12] |
Keith Burns, Amie Wilkinson. Dynamical coherence and center bunching. Discrete & Continuous Dynamical Systems - A, 2008, 22 (1&2) : 89-100. doi: 10.3934/dcds.2008.22.89 |
[13] |
Irene Márquez-Corbella, Edgar Martínez-Moro, Emilio Suárez-Canedo. On the ideal associated to a linear code. Advances in Mathematics of Communications, 2016, 10 (2) : 229-254. doi: 10.3934/amc.2016003 |
[14] |
Serhii Dyshko. On extendability of additive code isometries. Advances in Mathematics of Communications, 2016, 10 (1) : 45-52. doi: 10.3934/amc.2016.10.45 |
[15] |
Yangyang Xu, Wotao Yin, Stanley Osher. Learning circulant sensing kernels. Inverse Problems & Imaging, 2014, 8 (3) : 901-923. doi: 10.3934/ipi.2014.8.901 |
[16] |
Vikram Krishnamurthy, William Hoiles. Information diffusion in social sensing. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 365-411. doi: 10.3934/naco.2016017 |
[17] |
José M. Arrieta, Esperanza Santamaría. Estimates on the distance of inertial manifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 3921-3944. doi: 10.3934/dcds.2014.34.3921 |
[18] |
Liliana Trejo-Valencia, Edgardo Ugalde. Projective distance and $g$-measures. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3565-3579. doi: 10.3934/dcdsb.2015.20.3565 |
[19] |
Michael Brin, Dmitri Burago, Sergey Ivanov. Dynamical coherence of partially hyperbolic diffeomorphisms of the 3-torus. Journal of Modern Dynamics, 2009, 3 (1) : 1-11. doi: 10.3934/jmd.2009.3.1 |
[20] |
Bernard Bonnard, Thierry Combot, Lionel Jassionnesse. Integrability methods in the time minimal coherence transfer for Ising chains of three spins. Discrete & Continuous Dynamical Systems - A, 2015, 35 (9) : 4095-4114. doi: 10.3934/dcds.2015.35.4095 |
2018 Impact Factor: 0.879
Tools
Metrics
Other articles
by authors
[Back to Top]