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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
https://izlik.org/JA24KN93JJ

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
https://izlik.org/JA24KN93JJ

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
Authors

Vladimir Edemskiy

Publication Date May 27, 2013
IZ https://izlik.org/JA24KN93JJ
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. https://izlik.org/JA24KN93JJ
AMA 1.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. https://izlik.org/JA24KN93JJ
Chicago Edemskiy, Vladimir. 2013. “The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences”. International Journal of Applied Mathematics Electronics and Computers 1 (4): 7-11. https://izlik.org/JA24KN93JJ.
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 [1]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, Dec. 2013, [Online]. Available: https://izlik.org/JA24KN93JJ
ISNAD Edemskiy, Vladimir. “The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences”. International Journal of Applied Mathematics Electronics and Computers 1/4 (December 1, 2013): 7-11. https://izlik.org/JA24KN93JJ.
JAMA 1.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, Dec. 2013, pp. 7-11, https://izlik.org/JA24KN93JJ.
Vancouver 1.Vladimir Edemskiy. The Linear Complexity and Autocorrelation of Quaternary Whiteman’s Sequences. International Journal of Applied Mathematics Electronics and Computers [Internet]. 2013 Dec. 1;1(4):7-11. Available from: https://izlik.org/JA24KN93JJ