New quaternary sequences of even length with optimal auto-correlation

Research Paper
  • 44 Downloads

Abstract

Sequences with low auto-correlation property have been applied in code-division multiple access communication systems, radar and cryptography. Using the inverse Gray mapping, a quaternary sequence of even length N can be obtained from two binary sequences of the same length, which are called component sequences. In this paper, using interleaving method, we present several classes of component sequences from twin-prime sequences pairs or GMW sequences pairs given by Tang and Ding in 2010; or two, three or four binary sequences defined by cyclotomic classes of order 4. Hence we can obtain new classes of quaternary sequences, which are different from known ones, since known component sequences are constructed from a pair of binary sequences with optimal auto-correlation or Sidel’nikov sequences.

Keywords

binary sequences quaternary sequences Gray mapping interleaving cyclotomy 

Notes

Acknowledgements

The work of Wei SU was supported by National Science Foundation of China (Grant No. 61402377), and in part supported by Open Research Subject of Key Laboratory (Research Base) of Digital Space Security (Grant No. szjj2014-075), and Science and Technology on Communication Security Laboratory (Grant No. 9140C110302150C11004). The work of Yang YANG was supported by National Science Foundation of China (Grants Nos. 61401376, 11571285), and Application Fundamental Research Plan Project of Sichuan Province (Grant No. 2016JY0160). The work of Zhengchun ZHOU and Xiaohu TANG was supported by National Science Foundation of China (Grants Nos. 61672028, 61325005).

References

  1. 1.
    Fan P Z, Darnell M. Sequences Design for Communication Applications. Australia and New Zealand: Jacaranda Wiley Ltd., 1996. 5–15Google Scholar
  2. 2.
    Golomb S W, Gong G. Signal Design for Good Correlation: for Wireless Communication. Cambridge: Cryptography and Radar Cambridge University Press, 2005. 1–438CrossRefMATHGoogle Scholar
  3. 3.
    Lüke H D, Schotten H D, Hadinejad-Mahram H. Binary and quadriphase sequence with optimal autocorrelation: a survey. IEEE Trans Inf Theory, 2003, 49: 3271–3282MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Schotten H D. Optimum complementary sets and quadriphase sequences derived form q-ary m-sequences. In: Proceedings of IEEE International Symposium on Information Theory, Ulm, 1997. 485CrossRefGoogle Scholar
  5. 5.
    Lüke H D, Schotten H D. Odd-perfect almost binary correlation sequences. IEEE Trans Aerosp Electron Syst, 1995, 31: 495–498CrossRefGoogle Scholar
  6. 6.
    Green D H, Green P R. Polyphase-related prime sequences. IEEE Proc Comput Digit Tech, 2001, 148: 53–62CrossRefGoogle Scholar
  7. 7.
    Li N, Tang X H, Helleseth T. New M-ary sequences with low autocorrelation from interleaved technique. Des Codes Cryptogr, 2014, 73: 237–249MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Sidelnikov V M. Some k-vauled pseudo-random sequences and nearly equidistant codes. Probl Inf Trans, 1969, 5: 12–16Google Scholar
  9. 9.
    Tang X H, Lindner J. Almost quadriphase sequence with ideal autocorrelation property. IEEE Signal Process Lett, 2009, 16: 38–40CrossRefGoogle Scholar
  10. 10.
    Yang Z, Ke P H. Quaternary sequences with odd period and low autocorrelation. Electron Lett, 2010, 46: 1068–1069CrossRefGoogle Scholar
  11. 11.
    Yang Z, Ke P H. Construction of quaternary sequences of length pq with low autocorrelation. Cryptogr Commun Discret Struct Boolean Funct Seq, 2011, 3: 55–64MathSciNetMATHGoogle Scholar
  12. 12.
    Tang X H, Ding C. New classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value. IEEE Trans Inf Theory, 2010, 56: 6398–6405MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Kim Y-S, Jang J-W, Kim S-H, et al. New quaternary sequences with optimal autocorrelation. In: Proceedings of the IEEE International Conference on Symposium on Information Theory, Seoul, 2009. 286–289Google Scholar
  14. 14.
    Lüke H D, Schotten H D, Hadinejad-Mahram H. Generalised Sidelnikov sequences with optimal autocorrelation properties. Electron Lett, 2000, 36: 525–527CrossRefMATHGoogle Scholar
  15. 15.
    Kim Y-S, Jang J-W, Kim S-H, et al. New construction of quaternary sequences with ideal autocorrelation from Legendre sequences. In: Proceedings of the IEEE international conference on Symposium on Information Theory, Seoul, 2009. 282–285Google Scholar
  16. 16.
    Jang J W, Kim Y S, Kim S H, et al. New quaternary sequences with ideal autocorrelation constructed from binary sequences with ideal autocorrelation. In: Proceedings of IEEE International Symposium on Information Theory, Seoul, 2009. 278–281Google Scholar
  17. 17.
    Tang X H, Gong G. New constructions of binary sequences with optimal autocorrelation value/magnitude. IEEE Trans Inf Theory, 2010, 56: 1278–1286MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Krone S M, Sarwate D V. Quadriphase sequences for spread spectrum multiple access communication. IEEE Trans Inf Theory, 1984, IT-30: 520–529MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Science China Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Wei Su
    • 1
    • 4
  • Yang Yang
    • 2
    • 4
  • Zhengchun Zhou
    • 2
  • Xiaohu Tang
    • 3
  1. 1.School of Economics and Information EngineeringSouthwestern University of Finance and EconomicsChengduChina
  2. 2.School of MathematicsSouthwest Jiaotong UniversityChengduChina
  3. 3.Provincial Key Lab of Information Coding and Transmission, Institute of Mobile CommunicationsSouthwest Jiaotong UniversityChengduChina
  4. 4.Science and Technology on Communication Security LaboratoryChengduChina

Personalised recommendations