\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Coherence of sensing matrices coming from algebraic-geometric codes

Abstract Related Papers Cited by
  • Compressed sensing is a technique which is to used to reconstruct a sparse signal given few measurements of the signal. One of the main problems in compressed sensing is the deterministic construction of the sensing matrix. Li et al. introduced a new deterministic construction via algebraic-geometric codes (AG codes) and gave an upper bound for the coherence of the sensing matrices coming from AG codes. In this paper, we give the exact value of the coherence of the sensing matrices coming from AG codes in terms of the minimum distance of AG codes and deduce the upper bound given by Li et al. We also give formulas for the coherence of the sensing matrices coming from Hermitian two-point codes.
    Mathematics Subject Classification: Primary: 11T71, 14G50; Secondary: 92C55, 11R58, 14H50.

    Citation:

    \begin{equation} \\ \end{equation}
  • [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.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(197) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return