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The Linear Complexity and Autocorrelation of Quaternary Whiteman's Sequences

Year 2013, Volume: 1 Issue: 4, 7 - 11, 27.05.2013

Abstract

We found the linear complexity of quaternary sequences of period over the ring Z_4 . The sequences are based on Whiteman's generalized cyclotomic classes of order four. Also we derived the maximum nontrivial autocorrelation magnitude of the constructed sequences.

References

  • E. Bai, X. Fu and G. Xiao, “On the linear complexity of generalized cyclotomic sequences of order four over ,” IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences, vol. E88-A(1), pp. 392-395, 2005.
  • T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, Elsevier, Amsterdam, 1998.
  • A. Çeçmelio lu and W. Meidl, “A general approach to construction and determination of the linear complexity of sequences based on cosets. Sequences and Their Applications - SETA 2010”, LNCS, vol. 6338, pp.125-138, 2010.
  • Z. Chen and X. Du, “Linear complexity and autocorrelation values of a polyphase generalized cyclotomic sequence of length ”, Frontiers of Computer Science in China, vol. 4 (4), pp. 529-535, 2010.
  • V. A. Edemskii, “ On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes,” Discret. Math. Appl., vol. 20(1), pp. 75–84, 2010 (Diskretn. Mat. 22(1), 74–82 (2010)).
  • D. H. Green and P. R. Green, “Polyphase power-residue sequences”, Proc. R. Soc. Lond. A., vol. 459, pp. 817—827, 2003.
  • D. H. Green, “Linear complexity of modulo-m power residue sequences”, IEE Proc., Comput. Digit. Tech., vol. 151 (6), pp. 385—390, 2004.
  • L. Hu, Q. Yue and M. Wang, “The Linear Complexity of Whiteman's Generalized Cyclotomic Sequences of Period ”, IEEE Trans. Info. Theory, vol. 58 (8), pp. 5534 – 5543, 2012.
  • W. Meidl, “Remarks on a cyclotomic sequence”, Des. Codes Cryptography, vol. 51(1), pp. 33-43, 2009.
  • H. Niederreiter, “Linear complexity and related complexity measures for sequences”,ed. T. Johansson, S. Maitra, INDOCRYPT 2003. LNCS, vol. 2904, pp. 1–17, 2003.
  • J. A. Reeds and N. J. A. Sloane, “Shift-register synthesis (modulo )”, SIAM J. Comput., vol. 14, pp. 505-513, 1968.
  • A. Topuzoўglu and A. Winterhof, “Pseudorandom sequences”, ed. A. Garcia, H. Stichtenoth, Topics in Geometry, Coding Theory and Cryptography, Algebra and Applications, vol. 6, pp. 135—166, 2007.
  • T. Yan, X. Du, G. Xiao and X. Huang, “Linear complexity of binary Whiteman generalized cyclotomic sequences of order ”, Information Sciences, vol. 179(7), pp.1019–-1023, 2009.
  • Z. Yang and P. Ke, “Construction of quaternary sequences of length pq with low autocorrelation”, Cryptography and Communications, vol. 3 (2), pp. 55-64, 2011.
  • W. Z. Wan, Finite Fields and Galois Rings, Singapore. World Scientific Publisher, 2003.
  • W. Z. Wan, Algebra and Coding Theory, Beijing. Science Press, 1976.
  • A. L. Whiteman, “ A family of diference sets”, Illinois J. Math., vol. 6, pp. 107-121, 1962.

Original Research Paper

Year 2013, Volume: 1 Issue: 4, 7 - 11, 27.05.2013

Abstract

References

  • E. Bai, X. Fu and G. Xiao, “On the linear complexity of generalized cyclotomic sequences of order four over ,” IEICE Trans. Fundamentals of Electronics, Communications and Computer Sciences, vol. E88-A(1), pp. 392-395, 2005.
  • T. W. Cusick, C. Ding and A. Renvall, Stream Ciphers and Number Theory, Elsevier, Amsterdam, 1998.
  • A. Çeçmelio lu and W. Meidl, “A general approach to construction and determination of the linear complexity of sequences based on cosets. Sequences and Their Applications - SETA 2010”, LNCS, vol. 6338, pp.125-138, 2010.
  • Z. Chen and X. Du, “Linear complexity and autocorrelation values of a polyphase generalized cyclotomic sequence of length ”, Frontiers of Computer Science in China, vol. 4 (4), pp. 529-535, 2010.
  • V. A. Edemskii, “ On the linear complexity of binary sequences on the basis of biquadratic and sextic residue classes,” Discret. Math. Appl., vol. 20(1), pp. 75–84, 2010 (Diskretn. Mat. 22(1), 74–82 (2010)).
  • D. H. Green and P. R. Green, “Polyphase power-residue sequences”, Proc. R. Soc. Lond. A., vol. 459, pp. 817—827, 2003.
  • D. H. Green, “Linear complexity of modulo-m power residue sequences”, IEE Proc., Comput. Digit. Tech., vol. 151 (6), pp. 385—390, 2004.
  • L. Hu, Q. Yue and M. Wang, “The Linear Complexity of Whiteman's Generalized Cyclotomic Sequences of Period ”, IEEE Trans. Info. Theory, vol. 58 (8), pp. 5534 – 5543, 2012.
  • W. Meidl, “Remarks on a cyclotomic sequence”, Des. Codes Cryptography, vol. 51(1), pp. 33-43, 2009.
  • H. Niederreiter, “Linear complexity and related complexity measures for sequences”,ed. T. Johansson, S. Maitra, INDOCRYPT 2003. LNCS, vol. 2904, pp. 1–17, 2003.
  • J. A. Reeds and N. J. A. Sloane, “Shift-register synthesis (modulo )”, SIAM J. Comput., vol. 14, pp. 505-513, 1968.
  • A. Topuzoўglu and A. Winterhof, “Pseudorandom sequences”, ed. A. Garcia, H. Stichtenoth, Topics in Geometry, Coding Theory and Cryptography, Algebra and Applications, vol. 6, pp. 135—166, 2007.
  • T. Yan, X. Du, G. Xiao and X. Huang, “Linear complexity of binary Whiteman generalized cyclotomic sequences of order ”, Information Sciences, vol. 179(7), pp.1019–-1023, 2009.
  • Z. Yang and P. Ke, “Construction of quaternary sequences of length pq with low autocorrelation”, Cryptography and Communications, vol. 3 (2), pp. 55-64, 2011.
  • W. Z. Wan, Finite Fields and Galois Rings, Singapore. World Scientific Publisher, 2003.
  • W. Z. Wan, Algebra and Coding Theory, Beijing. Science Press, 1976.
  • A. L. Whiteman, “ A family of diference sets”, Illinois J. Math., vol. 6, pp. 107-121, 1962.
There are 17 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Vladimir Edemskiy

Publication Date May 27, 2013
Published in Issue Year 2013 Volume: 1 Issue: 4

Cite

APA Edemskiy, V. (2013). The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences. International Journal of Applied Mathematics Electronics and Computers, 1(4), 7-11.
AMA Edemskiy V. The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences. International Journal of Applied Mathematics Electronics and Computers. December 2013;1(4):7-11.
Chicago Edemskiy, Vladimir. “The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences”. International Journal of Applied Mathematics Electronics and Computers 1, no. 4 (December 2013): 7-11.
EndNote Edemskiy V (December 1, 2013) The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences. International Journal of Applied Mathematics Electronics and Computers 1 4 7–11.
IEEE V. Edemskiy, “The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences”, International Journal of Applied Mathematics Electronics and Computers, vol. 1, no. 4, pp. 7–11, 2013.
ISNAD Edemskiy, Vladimir. “The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences”. International Journal of Applied Mathematics Electronics and Computers 1/4 (December 2013), 7-11.
JAMA Edemskiy V. The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences. International Journal of Applied Mathematics Electronics and Computers. 2013;1:7–11.
MLA Edemskiy, Vladimir. “The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences”. International Journal of Applied Mathematics Electronics and Computers, vol. 1, no. 4, 2013, pp. 7-11.
Vancouver Edemskiy V. The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences. International Journal of Applied Mathematics Electronics and Computers. 2013;1(4):7-11.