Skip to main content
SpringerLink
Log in

Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes

  • Original Paper
  • Published:
Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract

Low-hit-zone frequency hopping sequence (LHZ-FHS) sets having optimal Hamming correlation are desirable in quasi-synchronous communication systems. In this paper, we first derive a new bound on maximum nontrivial Hamming correlation of LHZ-FHS sets from the famous Singleton bound in error correcting code literature, then obtain a general construction of LHZ-FHS sets from cyclic codes. Especially, two classes of LHZ-FHS sets meeting the new bound are constructed from punctured Reed-Solomon codes.

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. Chung, J., Yang, K.: New classes of optimal low-hit-zone frequency-hopping sequence sets by cartesian product. IEEE Trans. Inform. Theory 59(1), 726–732 (2013)

    Article  MathSciNet  Google Scholar 

  2. Ding, C., Fuji-Hara, R., Fujiwara, Y., Jimbo, J., Mishima, M.: Sets of frequency-hopping sequences: bounds and optimal constructions. IEEE Trans. Inform. Theory 55(7), 3297–3304 (2009)

    Article  MathSciNet  Google Scholar 

  3. Golomb, S.W.: A mathematical theory of discrete classification. In Proceedings of the London Symposium (1961)

  4. Golomb, S.W., Gordon, B., Welch, L.R.: Comma-free codes. Can. J. Math. 10, 202–209 (1958)

    Article  MathSciNet  Google Scholar 

  5. Han, H., Peng, D., Parampalli, U., Ma, Z., Liang, H.: Construction of low-hit-zone frequency-hopping sequences with optimal partial Hamming correlation by interleaving techniques. Des. Codes Cryptogr. 84, 404–414 (2017)

    Article  MathSciNet  Google Scholar 

  6. Lin, S., Xing, C.: Coding Theory: A First Course. Cambridge University Press, Cambridge (2004)

    Google Scholar 

  7. Ling, L., Niu, X., Zeng, B., Liu, X.: New classes of optimal low-hit-zone frequency-hopping sequence set with large family size. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 101–A, 2213–2216 (2018)

    Google Scholar 

  8. Ma, W., Sun, S.: New designs of frequency-hopping sequences with low-hit-zone. Des. Codes Cryptogr. 60, 145–153 (2011)

    Article  MathSciNet  Google Scholar 

  9. Niu, H., Peng, D., Zhou, C.: New classes of optimal frequency-hopping sequences with low-hit-zone with New Parameters. In: IWSDA, Guilin, China, pp. 111–114 (2011)

  10. Niu, X., Peng, D., Han, H.: Low-hit-zone frequency-hopping sequence sets with optimal partial Hamming correlation properties. Des. Codes Cryptogr. 73, 167–176 (2014)

    Article  MathSciNet  Google Scholar 

  11. Scholtz, R.A.: The spread spectrum concept. IEEE Trans. Inform. Theory 25(8), 748–755 (1977)

    MATH  Google Scholar 

  12. Song, H., Golomb, S.W.: On the nonperiodic cyclic equivalence classes of Reed-Solomon codes. IEEE Trans. Inform. Theory 39(4), 1431–1434 (1993)

    Article  Google Scholar 

  13. Wang, C., Peng, D., Han, H., Zhou, L.: New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation. Sci. China (Inf. Sci.) 58, 162–176 (2015)

    Google Scholar 

  14. Wang, C., Peng, D., Zhou, L.: New constructions of optimal frequency-hopping sequence sets with low-hit-zone. Int. J. Found. Comput. Sci. 27(1), 53–66 (2016)

    Article  MathSciNet  Google Scholar 

  15. Wang, X., Fan, P.: A class of frequency-hopping sequences with no-hit-zone. In: PDCAT, Chengdu, China, pp. 896–898 (2003)

  16. Yang, Y., Tang, X., Parampalli, U., Peng, D.: New bound on frequency-hopping sequence sets and its optimal constructions. IEEE Trans. Inform. Theory 57(11), 7605–7613 (2011)

    Article  MathSciNet  Google Scholar 

  17. Zhou, L., Peng, D., Liang, H., Wang, Y., Ma, Z.: Constructions of optimal low-hit-zone frequency-hopping sequence sets. Des. Codes Cryptogr. 85, 219–232 (2017)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are very grateful to the Editor and the anonymous reviewer for careful reading and invaluable suggestions that improved the quality of this paper. This work was supported by the Natural Science Foundation of China under Grant 11971395, and was supported by the Projects of Central Government to Guide Local Scientific and Technological Development under Grant 2021ZYD0001.

Author information

Authors and Affiliations

  1. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Cuiling Fan & Xiaoxiao Cui

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

    Wei Su

Authors
  1. Cuiling Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoxiao Cui
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Su
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Su.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, C., Cui, X. & Su, W. Constructions of low-hit-zone frequency hopping sequence sets from cyclic codes. AAECC (2022). https://doi.org/10.1007/s00200-022-00581-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00200-022-00581-4

Keywords

Mathematics Subject Classification

Search

Navigation