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Correlation Functions of Perfect Binary Sequences of Same Lengths

  • Zepeng ZhuoEmail author
  • Jinfeng Chong
  • Lei Yu
  • Zhiyao Yang
Computer Science
  • 22 Downloads

Abstract

The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among cross-correlation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.

Key words

binary sequence perfect sequence cross-correlation function autocorrelation function 

CLC number

TN 914. 5 

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References

  1. [1]
    No J S, Golomb S W, Gong G, et al. Binary pseudo-random sequences of period 2n -1 with ideal autocorrelation [J]. IEEE Transactions on Information Theory, 1998, 1998(2): 814–817.Google Scholar
  2. [2]
    Mercer I. Autocorrelations of random binary sequences [J]. Combinatorics Probability and Computing, 2006, 2006(15): 663–671.CrossRefGoogle Scholar
  3. [3]
    Peng X, Xu C, Li G, et al. The construction of almost binary sequences pairs and binary sequences pairs with three-level autocorrelation [J]. IEICE Transactions on Fundamentals of Electronic Communications and Computer Sciences, 2011, 94-A(9): 1886–1891.CrossRefGoogle Scholar
  4. [4]
    Meng R F, Yan T J. New constructions of binary interleaved sequences with low autocorrelation [J]. International Journal of Network Security, 2017, 2017(4): 546–550.Google Scholar
  5. [5]
    Yu N Y, Gong G. The perfect binary sequence of period 4 for low periodic and aperiodic autocorrelations [C]// SSC 2007. Heidelberg: Springer-Verlag, 2007: 37–49.Google Scholar
  6. [6]
    Helleseth T. Some results about the cross-correlation function between two maximal linear sequences [J]. Discrete Mathematics, 1976, 1976(3): 209–232.CrossRefGoogle Scholar
  7. [7]
    Helleseth T, Kumar P V. Handbook of Coding Theory [M]. Amsterdam: Elsevier, 1998.Google Scholar
  8. [8]
    Chong J F, Zhuo Z P. Cross-correlation properties of some perfect binary sequences [C]// 2011 IEEE International Conference on Computer Science and Automation Engineering. Piscataway: IEEE, 2011: 654–657.CrossRefGoogle Scholar
  9. [9]
    Hertel D. Cross-correlation properties of perfect binary sequences [C]// SETA 2004. Heidelberg: Springer-Verlag, 2005: 208–219.Google Scholar
  10. [10]
    Golomb S W, Gong G. Signal Design for Good Correlation for Wireless Communication, Cryptography, and Radar [M]. Cambridge: Cambridge University Press, 2005.CrossRefGoogle Scholar
  11. [11]
    Sarwate D V. Bounds on cross-correlation and autocorrelation of sequences [J]. IEEE Transactions on Information Theory, 1979, 1979(6): 720–724.CrossRefGoogle Scholar
  12. [12]
    Pursley M B. Performance evaluation for phase-coded spread-spectrum multiple-access communication — Part I: System analysis [J]. IEEE Transactions on Communications, 1977, 1977(8): 795–799.CrossRefGoogle Scholar

Copyright information

© Wuhan University and Springer-Verlag GmbH Germany 2019

Authors and Affiliations

  • Zepeng Zhuo
    • 1
    Email author
  • Jinfeng Chong
    • 1
    • 2
  • Lei Yu
    • 3
  • Zhiyao Yang
    • 1
  1. 1.School of Mathematical ScienceHuaibei Normal UniversityHuaibei, AnhuiChina
  2. 2.Information CollegeHuaibei Normal UniversityHuaibei, AnhuiChina
  3. 3.School of Computer Science and TechnologyHuaibei Normal UniversityHuaibei, AnhuiChina

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