Skip to main content
Springer Nature Link
Log in

New p-ary sequence family with low correlation and large linear span

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, for an odd prime p and positive integers n, m, and e such that n = me, a new family \({\mathcal{S}}\) of p-ary sequences of period p n − 1 with low correlation and large linear span is constructed. It is shown that \({\mathcal{S}}\) has maximum correlation \({1+p^{n+2e\over 2}}\), family size p n, and maximal linear span \({{(m+3)n\over 2}}\). When m is even, the proposed family \({\mathcal{S}}\) contains Tang, Udaya, and Fan’s construction as a subset. Furthermore, when n is even and \({e=1, \mathcal{S}}\) has the same correlation and family size, but larger linear span compared with the construction by Seo, Kim, No, and Shin.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Golomb S.W., Gong G.: Signal Designs for Good Correlation—for Wireless Communications, Cryptography and Radar Applications. Cambridge University Press, New York (2005)

    Book  Google Scholar 

  2. Helleseth T.: Some results about the cross-correlation function between two maximal linear sequences. Discrete Math. 16(3), 209–232 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  3. Helleseth T., Kumar P.V.: Sequences with low correlation. In: Pless, V., Huffman, C. (eds) Handbook of Coding Theory, pp. 1767–1853. Elservier, Amsterdam (1998)

    Google Scholar 

  4. Jang J., Kim Y.K., No J.S., Helleseth T.: New family of p-ary sequences with optimal correlation property and large linear span. IEEE Trans. Inform. Theory 50(8), 1839–1844 (2004)

    Article  MathSciNet  Google Scholar 

  5. Key E.L.: An analysis of the structure and complexity of nonlinear binary sequence generators. IEEE Trans. Inform. Theory 22(6), 732–736 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kumar P.V., Moreno O.: Prime-phase sequences with periodic correlation properties better than binary sequences. IEEE Trans. Inform. Theory 37(3), 603–616 (1991)

    Article  MathSciNet  Google Scholar 

  7. Lidl R., Niederreiter H.: Finite Fields. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  8. Liu S.-C., Komo J.F.: Nonbinary Kasami sequences over GF(p). IEEE Trans. Inform. Theory 38(4), 1409–1412 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  9. Moriuchi T., Imamura K.: Balanced nonbinary sequences with good periodic correlation properties obtained from modified Kumar-Moreno sequences. IEEE Trans. Inform. Theory 41(2), 572–576 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  10. Seo E.Y., Kim Y.S., No J.S., Shin D.J.: Cross-correlation distribution of p-ary m-sequence and its p + 1 decimated sequences with shorter period. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E90-A(11), 2568–2574 (2007)

    Article  Google Scholar 

  11. Sidelnikov V.M.: On mutual correlation of sequences. Soviet Math. Dokl. 12(1), 197–201 (1971)

    Google Scholar 

  12. Tang X.H., Udaya P., Fan P.Z.: A new family of nonbinary sequences with three-level correlation property and large linear span. IEEE Trans. Inform. Theory 51(5), 2906–2914 (2005a)

    Article  MathSciNet  Google Scholar 

  13. Tang X.H., Udaya P., Fan P.Z.: New families of p-ary sequences from quadratic form with low correlation and large linear span. Lect. Notes Comput. Sci. 3486, 255–265 (2005b)

    Article  Google Scholar 

  14. Trachtenberg, H.M.: On the crosscorrelation functions of maximal linear recurring sequences. Ph.D. dissertation, University of Southern California, Los Angeles (1970)

Download references

Author information

Authors and Affiliations

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

    Zhengchun Zhou

  2. State Key Laboratory of Information Security, Institute of Software, Chinese Academy of Sciences, Beijing, China

    Zhengchun Zhou

  3. Institute of Mobile Communications, Southwest Jiaotong University, Chengdu, 610031, China

    Xiaohu Tang & Daiyuan Peng

  4. Department of Computer Science and Software Engineering, University of Melbourne, 3010, Parkville, VIC, Australia

    Udaya Parampalli

Authors
  1. Zhengchun Zhou
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Xiaohu Tang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Udaya Parampalli
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Daiyuan Peng
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Zhengchun Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, Z., Tang, X., Parampalli, U. et al. New p-ary sequence family with low correlation and large linear span. AAECC 22, 301–309 (2011). https://doi.org/10.1007/s00200-011-0151-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00200-011-0151-7

Keywords