Skip to main content
SpringerLink
Log in

Special Distribution of the Shortest Linear Recurring Sequences in Z /(p) Field

  • Conference paper
Computational Intelligence and Security (CIS 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3802))

Included in the following conference series:

Abstract

In this paper, the distribution of the shortest linear recurring sequences in Z /(p) is studied. It is found that the shortest linear recurrent length is always equal to n / 2 when n is even and is always equal to n / 2+1 when n is odd for any sequence whose length is n. In other words, the shortest linear recurring length is always equal to the half of the length of the given sequence. The probability of finding the distribution of the shortest linear recurring length of two sequences in Z / (p) field is also given.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Meidl, W.: On the Stability of 2n-Periodic Binary Sequences. IEEE Trans. Inform Theory, IT-51(3), 1151–1155 (2005)

    Article  MathSciNet  Google Scholar 

  2. Reeds, J.A., Sloane, N.J.A.: Shift-register synthesis (modulo m). SIAM Journal on Computing 14(3), 505–513 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  3. Dingfeng, Y., Zongduo, D.: Periodic sequence linear order of complexity under two marks replacing. In: Fourth session of Chinese cryptology academic conference collection (1996) (in Chinese)

    Google Scholar 

  4. Yujie, Z., Jinjun, Z.: The relationship between two kinds of sequences syntheses algorithm over ring Z/(m). In: Fifth session of Chinese cryptology academic conference collection (1998) (in Chinese)

    Google Scholar 

  5. Liying, G., Yuefei, Z.: The shortest linear recurrence of two sequences. Journal of information engineering university 2(1), 17–22 (2001) (in Chinese)

    Google Scholar 

  6. Guiliang, F., Tzeng, K.K.A.: Generalization of the Berlekamp-Massey algorithm for multi-sequence shift-register synthesis with applications to decoding cyclic codes. IEEE Trans. Inform. Theory 37(5), 1274–1287 (1991)

    Article  MathSciNet  Google Scholar 

  7. Guiliang, F., Tzeng, K.K.A.: Generalized Euclidean algorithm for multi-sequence shift-register synthesis. IEEE Trans. Inform. Theory 35(3), 584–594 (1989)

    Article  MathSciNet  Google Scholar 

  8. Jinjun, Z., Wenfeng, Q., Yujie, Z.: Gröbner base extension and Multi-sequences comprehensive algorithm over Z/(m). Science in China, 113–120 (1995) (in Chinese)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, College of Information Science and Technology, Beijing Normal University, Beijing, 100875, China

    Qian Yin, Yunlun Luo & Ping Guo

Authors
  1. Qian Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yunlun Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ping Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Microelectronic Instiute, Xidian University, 710071, Xi’an, China

    Yue Hao

  2. Department of Computer Science, Hong Kong Baptist University, Kowloon Tong, Hong Kong

    Jiming Liu

  3. School of Computer Science and Technology, Xidian University, Xi’an, China

    Yu-Ping Wang

  4. Department of Computer Science, Hong Kong Baptist University, Hong Kong,  

    Yiu-ming Cheung

  5. School of Electrical and Electronic Engineering, University of Manchester, UK

    Hujun Yin

  6. Life Science Research Center, School of Electronic Engineering, Xidian University, 710071, Xi’an, Shaanxi, China

    Licheng Jiao

  7. Key Laboratory of Computer Networks and Information Security(Ministry of Education), Xidian University, 710071, Xi’an, China

    Jianfeng Ma

  8. National Laboratory of Antennas and Microwave Technology, Xidian University, 710071, Xi’an, Shanxi, P.R. China

    Yong-Chang Jiao

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Yin, Q., Luo, Y., Guo, P. (2005). Special Distribution of the Shortest Linear Recurring Sequences in Z /(p) Field. In: Hao, Y., et al. Computational Intelligence and Security. CIS 2005. Lecture Notes in Computer Science(), vol 3802. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11596981_6

Download citation

  • DOI: https://doi.org/10.1007/11596981_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30819-5

  • Online ISBN: 978-3-540-31598-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation