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

Correlation of binary sequence families derived from the multiplicative characters of finite fields

Abstract / Introduction Related Papers Cited by
  • In this paper, new constructions of the binary sequence families of period $q-1$ with large family size and low correlation, derived from multiplicative characters of finite fields for odd prime powers, are proposed. For $m ≥ 2$, the maximum correlation magnitudes of new sequence families $\mathcal{S}_m$ are bounded by $(2m-2)\sqrt{q}+2m+2$, and the family sizes of $\mathcal{S}_m$ are given by $q-1$ for $m=2$, $2(q-1)-1$ for $m=3$, $(q^2-1)q^{\frac{m-4}{2}}$ for $m$ even, $m>2$, and $2(q-1)q^{\frac{m-3}{2}}$ for $m$ odd, $m>3$. It is shown that the known binary Sidel'nikov-based sequence families are equivalent to the new constructions for the case $m=2$.
    Mathematics Subject Classification: Primary: 94B25, 11T24.

    Citation:

    \begin{equation} \\ \end{equation}
  • [1]

    P. Deligne, La conjecture de Weil I, Publ. Math. IHES, 43 (1974), 273-307.

    [2]

    S. W. Golomb and G. Gong, Signal Design with Good Correlation: for Wireless Communications, Cryptography and Radar Applications, Cambridge University Press, 2005.doi: 10.1017/CBO9780511546907.

    [3]

    L. Goubin, C. Mauduit and A. Sárközy, Construction of large families of pseudorandom binary sequences, J. Number Theory, 106 (2004), 56-69.doi: 10.1016/j.jnt.2003.12.002.

    [4]

    Y. K. Han and K. Yang, New $M$-ary sequence families with low correlation and large size, IEEE Trans. Inf. Theory, 55 (2009), 1815-1823.doi: 10.1109/TIT.2009.2013040.

    [5]

    T. Helleseth and P. V. Kumar, Sequences with low correlation, in Handbook of Coding Theory (eds. V. Pless and C. Huffman), Elsevier Science Publishers, 1998, 1765-1853.

    [6]

    Y. Kim, J. Chung, J. S. No and H. Chung, New families of $M$-ary sequences with low correlation constructed from Sidel'nikov sequences, IEEE Trans. Inf. Theory, 54 (2008), 3768-3774.doi: 10.1109/TIT.2008.926428.

    [7]

    Y. J. Kim and H. Y. Song, Cross correlation of Sidel'nikov sequences and their constant multiples, IEEE Trans. Inf. Theory, 53 (2007), 1220-1224.doi: 10.1109/TIT.2006.890723.

    [8]

    Y. J. Kim, H. Y. Song, G. Gong and H. Chung, Crosscorrelation of $q$-ary power residue sequences of period $p$, in Proc. IEEE ISIT, 2006, 311-315.doi: 10.1109/ISIT.2006.261604.

    [9]

    P. V. Kumar, T. Helleseth, A. R. Calderbank and A. R. Hammons, Large families of quaternary sequences with low correlation, IEEE Trans. Inf. Theory, 42 (1996), 579-592.doi: 10.1109/18.485726.

    [10]

    V. M. Sidel'nikov, Some $k$-valued pseudo-random sequences and nearly equidistant codes, Probl. Inf. Transm., 5 (1969), 12-16.

    [11]

    V. M. Sidel'nikov, On mutual correlation of sequences, Soviet Math. Dokl, 12 (1971), 197-201.

    [12]

    D. Wan, Generators and irreducible polynomials over finite fields, Math. Comput., 66 (1997), 1195-1212.doi: 10.1090/S0025-5718-97-00835-1.

    [13]

    Z. Wang and G. Gong, New polyphase sequence families with low correlation derived from the Weil bound of exponential sums, IEEE Trans. Inf. Theory, 59 (2013), 3990-3998.doi: 10.1109/TIT.2013.2243496.

    [14]

    A. Weil, On some exponential sums, Proc. Natl. Acad. Sci. USA, 34 (1948), 204-207.doi: 10.1073/pnas.34.5.204.

    [15]

    L. R. Welch, Lower bounds on the minimum correlation of signal, IEEE Trans. Inf. Theory, 20 (1974), 397-399.

    [16]

    N. Y. Yu and G. Gong, Multiplicative characters, the Weil Bound, and polyphase sequence families with low correlation, IEEE Trans. Inf. Theory, 56 (2010), 6376-6387.doi: 10.1109/TIT.2010.2079590.

    [17]

    N. Y. Yu and G. Gong, New construction of $M$-ary sequence families with low correlation from the structure of Sidelnikov sequences, IEEE Trans. Inf. Theory, 56 (2010), 4061-4070.doi: 10.1109/TIT.2010.2050793.

  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(97) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return