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On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length 2p m

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Abstract

In this article, new classes of generalized cyclotomic binary sequences with period 2p m are proposed. We determine the linear complexity and autocorrelation of these sequences. The results show that the proposed generalized cyclotomic binary sequences have high linear complexity, but do not have desirable autocorrelation properties.

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References

  1. Burton D.M.: Elementary Number Theory, 4th edn. McGraw-Hill International Editions, New York (1998)

    MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Cusick T., Ding C., Renvall A.: Stream ciphers and number theory. N.-Holl. Math. Libr. 55, 198–212 (1998)

    MathSciNet  Google Scholar 

  4. Ding C.: Linear complexity of some generalized cyclotomic sequences. Int. J. Algebra Comput. 8(4), 431–442 (1998)

    Article  MATH  Google Scholar 

  5. Ding C., Helleseth T.: Generalized cyclotomy and its applications. Finite Fields Appl. 4, 467–474 (1999)

    Google Scholar 

  6. Ding C., Hellseth T., Shan W.: On the linear complexity of Legendre sequences. IEEE Trans. Inform. Theory 44, 1276–1278 (1998)

    Article  MathSciNet  Google Scholar 

  7. Golomb S.W., Gong G.: Signal Design for Good Correlation: For Wireless Communications, Cryptography and Radar Applications. Cambridge University Press, Cambridge (2005)

    Book  Google Scholar 

  8. Kim Y.J., Jin S.Y., Song H.Y.: Linear complexity and autocorrelation of prime cube sequences. In: Boztas S., Lu H.-F. (eds.) AAECC 2007. LNCS, 4851, pp. 188–197. Springer, Heidelberg (2007).

  9. Kim Y.J., Song H.Y.: Linear complexity of prime n-square sequences. In: IEEE International Symposium on Information Theory, Toronto, Canada, pp. 2405–408 (2008).

  10. Massey J.L.: Shift register synthesis and BCH decoding. IEEE Trans. Inform. Theory 15(1), 122–127 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  11. Nathanson M.B.: Elementary Methods in Number Theory. Springer, Berlin (2003) GTM 195

    Google Scholar 

  12. Vladimir E.: About computation of the linear complexity of generalized cyclotomic sequences with period p n+1. Des. Codes Cryptogr. 61(3), 251–260 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Yan T., Sun R., Xiao G.: Autocorrelation and linear complexity of the new generalized cyclotomic sequences. IEICE Trans. Fundam. E90-A, 857–64 (2007).

  14. Yan T., Li S., Xiao G.: On the linear complexity of generalized cyclotomic sequences with the period pm. Appl. Math. Lett. 21, 187–193 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zhang J.W., Zhao C.A., Ma X.: Linear complexity of generalized cyclotomic binary sequences of length 2p m. AAECC 21, 93–108 (2010)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou, Fujian, 350007, People’s Republic of China

    Pinhui Ke & Shengyuan Zhang

  2. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, People’s Republic of China

    Jie Zhang

Authors
  1. Pinhui Ke
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  2. Jie Zhang
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  3. Shengyuan Zhang
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Corresponding author

Correspondence to Pinhui Ke.

Additional information

Communicated by T. Helleseth.

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Ke, P., Zhang, J. & Zhang, S. On the linear complexity and the autocorrelation of generalized cyclotomic binary sequences of length 2p m . Des. Codes Cryptogr. 67, 325–339 (2013). https://doi.org/10.1007/s10623-012-9610-9

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  • DOI: https://doi.org/10.1007/s10623-012-9610-9

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