Advanced Search
Article Contents
Article Contents

New complementary sets of length $2^m$ and size 4

Abstract Related Papers Cited by
  • We construct new complementary sequence sets of size $4$, using a graphical description. We explain how the construction can be seen as a special case of a less explicit array construction by Parker and Riera and, at the same time, a generalization of another construction by the same authors. Some generalizations of the construction are also given, which are not in the construction of Parker and Riera. Lower bounds and upper bounds of the number of sequences in the constructions are analyzed.
    Mathematics Subject Classification: Primary: 94A55, 68P30; Secondary: 05A15.


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

    S. Z. Budĭsin, P. Spasojević, Paraunitary generation/correlation of QAM complementary sequence pairs, Cryptogr. Commun., 6 (2014), 59-102.doi: 10.1007/s12095-013-0087-9.


    C.-Y. Chen, C.-H. Wang, and C.-C. Chao, Complementary sets and Reed-Muller codes for peak-to-average power ratio reduction in OFDM, in Int. Symp. Appl. Algebra Algebr. Algor. Error-Corr. Codes, Springer, Berlin, 2006, 317-327.doi: 10.1007/11617983_31.


    J. A. Davis and J. Jedwab, Peak-to-mean power control for OFDM, Golay complementary sequences, and Reed-Muller codes, IEEE Trans. Inform. Theory, 45 (1999), 2397-2417.doi: 10.1109/18.796380.


    F. Fiedler, J. Jedwab and M. G. Parker, A framework for the construction of Golay sequences, IEEE Trans. Inform. Theory, 54 (2008), 3113-3129.doi: 10.1109/TIT.2008.924667.


    F. Fiedler, J. Jedwab and M. G. Parker, A multi-dimensional approach to the construction and enumeration of Golay complementary sequences, J. Combin. Theory Ser. A, 115 (2008), 753-776.doi: 10.1016/j.jcta.2007.10.001.


    M. J. E. Golay, Complementary series, IEEE Trans. Inform. Theory, 7 (1961), 82-87.


    S. Litsyn, Peak Power Control in Multi-carrier Communications, Cambridge Univ. Press, 2007.


    M. G. Parker and C. Riera, Generalised complementary arrays, IMA Int. Conf. Crypt. Coding, Springer, Berlin, 2011, 41-60.doi: 10.1007/978-3-642-25516-8_4.


    M. G. Parker and C. Tellambura, Golay-Davis-Jedwab complementary sequences and Rudin-Shapiro constructions, in Int. Symp. Inform. Theory, 2001, 302.


    M. G. Parker and C. Tellambura, A construction for binary sequence sets with low peak-to-average power ratio, Reports in Informatics, Univ. Bergen, 2003.


    K. G. Paterson, Generalized Reed-Muller codes and power control in OFDM modulation, IEEE Trans. Inform. Theory, 46 (2000), 104-120.doi: 10.1109/18.817512.


    K.-U. Schmidt, On cosets of the generalized first-order Reed-Muller code with low PMEPR, IEEE Trans. Inform. Theory, 52 (2006), 3220-3232.doi: 10.1109/TIT.2006.876252.


    K.-U. Schmidt, Complementary sets, generalized Reed-Muller codes, and power control for OFDM, IEEE Trans. Inform. Theory, 53 (2007), 808-814.doi: 10.1109/TIT.2006.889723.


    T. E. Stinchcombe, Aperiodic autocorrelations of length $2^m$ sequences, complementarity, and power control for OFDM, Ph.D. thesis, Univ. London, 2000.


    Z. Wang, M. G. Parker, G. Gong and G. Wu, On the PMEPR of the binary Golay sequences of length $2^n$, IEEE Trans. Inform. Theory, 60 (2014), 2391-2398.doi: 10.1109/TIT.2014.2300867.


    Z. Wang, G. Wu and H. Li, Improved PMEPR bound on near-complementary sequences constructed by Yu and Gong, Electr. Lett., 49 (2013), 73-75.


    G. Wu and M. G. Parker, A complementary construction using mutually unbiased bases, Crypt. Commun., 6 (2014), 3-25.doi: 10.1007/s12095-013-0095-9.


    G. Wu, Y. Zhang and Z. Wang, Construction of near-complementary sequences with low PMEPR for peak power control in OFDM, IEICE Trans. Fundam., E95-A (2012), 1881-1887.


    N. Y. Yu and G. Gong, Near-complementary sequences with low PMEPR for peak power control in multicarrier communications, IEEE Trans. Inform. Theory, 57 (2011), 505-513.doi: 10.1109/TIT.2010.2090230.

  • 加载中

Article Metrics

HTML views() PDF downloads(189) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint