Autocorrelation of two Legendre-Sidelnikov sequences |
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| Authors: | XIE Jia, GAO Jun-tao, YUE Zhao, LI Xue-lian |
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| Affiliation: | [1]The State Key Laboratory of Integrated Services Network, Xidian University, Xi'an 710071, China; [2]Department of Mathematics, Xidian University, Xi'an 710071, China; [3]State Key Laboratory of Information Security Chinese Academy of Sciences, Beijing 100190, China |
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| 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. |
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| Keywords: | autocorrelation pseudo-randomness binary sequence quadratic character Legendre-Sidelnikov sequence two-prime generator |
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