Skip to main content
SpringerLink
Log in

New optimal binary sequences with period 4p via interleaving Ding–Helleseth–Lam sequences

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

Binary sequences play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation value/magnitude has been an interesting research topic in sequence design. Ding–Helleseth–Lam sequences are such a class of binary sequences of period p, where p is an odd prime with \(p\equiv 1(\bmod ~4)\). The objective of this paper is to present a construction of binary sequences of period 4p via interleaving four suitable Ding–Helleseth–Lam sequences. This construction generates new binary sequences with optimal autocorrelation magnitude, which can not be produced by earlier ones.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arasu K.T., Ding C., Helleseth T., Kumar P.V., Martinsen H.: Almost difference sets and their sequences with optimal autocorrelation. IEEE Trans. Inf. Theory 47(7), 2834–2843 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  2. Cai Y., Ding C.: Binary sequences with optimal autocorrelation. Theoret. Comput. Sci. 410, 2316–2322 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  3. Ding C., Helleseth T., Lam K.Y.: Several classes of sequences with three-level autocorrelation. IEEE Trans. Inf. Theory 45(7), 2606–2612 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  4. Ding C., Helleseth T., Martinsen H.: New families of binary sequences with optimal three-level autocorrelation. IEEE Trans. Inf. Theory 47(1), 428–433 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  5. Golomb S.W., Gong G.: Signal Design for Good Correlation: for Wireless Communication, Cryptography and Radar. Cambridge University Press, Cambridge (2005).

    Book  MATH  Google Scholar 

  6. Gong G.: Theory and applications of \(q\)-ary interleaved sequences. IEEE Trans. Inf. Theory 41(2), 400–411 (1995).

    Article  MathSciNet  MATH  Google Scholar 

  7. Krengel E.I., Ivanov P.V.: Two constructions of binary sequences with optimal autocorrelation magnitude. Electron. Lett. 52(17), 1457–1459 (2016).

    Article  Google Scholar 

  8. Lempel A., Cohn M., Eastman W.L.: A class of binary sequences with optimal autocorrelation properties. IEEE Trans. Inf. Theory 23(1), 38–42 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  9. Li N., Tang X.H.: On the linear complexity of binary sequences of period \(4N\) with optimal autocorrelation value/magnitude. IEEE Trans. Inf. Theory 57(11), 7597–7604 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  10. No J.S., Chung H., Song H.Y., Yang K., Lee J.D., Helleseth T.: New construction for binary sequences of period \(p^m-1\) with optimal autocorrelation using \((z+1)^d+z^d+b\). IEEE Trans. Inf. Theory 47(4), 1638–1644 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  11. Sidelnikov V.M.: Some \(k\)-vauled pseudo-random sequences and nearly equidistant codes. Probl. Inf. Trans. 5, 12–16 (1969).

    Google Scholar 

  12. Su W., Yang Y., Zhou Z.C., Tang X.H.: New quaternary sequences of even length with optimal auto-correlation. Sci. China Inform. Sci. (2017). doi:10.1007/s11432-016-9087-2.

  13. Tang X.H., Ding C.: New classes of balanced quaternary and almost balanced binary sequences with optimal autocorrelation value. IEEE Trans. Inf. Theory 56(12), 6398–6405 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  14. Tang X.H., Gong G.: New constructions of binary sequences with optimal autocorrelation value/magnitude. IEEE Trans. Inf. Theory 56(3), 1278–1286 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  15. Wolfmann J.: Almost perfect autocorrelation sequences. IEEE Trans. Inf. Theory 38(4), 1412–1418 (1992).

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu N.Y., Gong G.: New binary sequences with optimal autocorrelation magnitude. IEEE Trans. Inf. Theory 54(10), 4771–4779 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang Y., Lei J.G., Zhang S.P.: A new family of almost difference sets and some necessary conditions. IEEE Trans. Inf. Theory 52(6), 2052–2061 (2006).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the reviewers and the Editor, Prof. Tor Helleseth, for their valuable comments that improved the presentation of this paper. The work of Wei Su was supported by the National Science Foundation of China under Grant 61402377. The work of Yang Yang and Cuiling Fan was partly supported by the National Science Foundation of China under Grants 11571285 and 6161101196, the China National 863 Project under Grant 2015AA01A710, and Application Fundamental Research Plan Project of Sichuan Province under Grant 2016JY0160.

Author information

Authors and Affiliations

  1. School of Economics and Information Engineering, Southwestern University of Finance and Economics, Chengdu, 610074, China

    Wei Su

  2. Collaborative Innovation Center for the Innovation and Regulation of Internet-based-Finance, Southwestern University of Finance and Economics, Chengdu, 610074, China

    Wei Su

  3. School of Mathematics, Southwest Jiaotong University, Chengdu, 611756, China

    Yang Yang & Cuiling Fan

Authors
  1. Wei Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yang Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cuiling Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yang Yang.

Additional information

Communicated by T. Helleseth.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, W., Yang, Y. & Fan, C. New optimal binary sequences with period 4p via interleaving Ding–Helleseth–Lam sequences. Des. Codes Cryptogr. 86, 1329–1338 (2018). https://doi.org/10.1007/s10623-017-0398-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10623-017-0398-5

Keywords

Mathematics Subject Classification

Search

Navigation