Acta Metallurgica Sinica(English letters) ›› 2014, Vol. 21 ›› Issue (5): 83-88.doi:

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Autocorrelation of two Legendre-Sidelnikov sequences

  

  • Received:2013-05-20 Revised:2014-06-19 Online:2014-10-31 Published:2014-10-30
  • Contact: Jia XIE E-mail:xiejia199325@163.com
  • Supported by:

    the Natural Science Foundation of China;Science and Technology on Communication Security Laboratory;The Fundamental Research Funds for the Central Universities

Abstract:  Sequences with nice pseudo-randomness play an important role in not only communication system but also cryptography system. Based on the Legendre-Sidelnikov sequence, a modified Legendre-Sidelnikov sequence was introduced. The exact value of the autocorrelation function was derived by strict computation. According to the values of the autocorrelation functions of the two Legendre-Sidelnikov sequences, it is proven that both of them have perfect pseudo-randomness. Furthermore, a detailed comparison between autocorrelation functions of the two Legendre-Sidelnikov sequences was deduced. It indicates that no matter which parameters are chosen, the modified sequence has pseudo-randomness as good as the primitive sequence, which is of great significance for applications.

Key words: autocorrelation, pseudo-randomness, binary sequence, quadratic character, Legendre-Sidelnikov sequence, two-prime generator

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