| Zpq上阶数为4的广义割圆序列及其自相关值 |
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| 引用本文： | 白恩健,刘晓娟.Zpq上阶数为4的广义割圆序列及其自相关值[J].工程数学学报,2008,25(5). |
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| 作者姓名： | 白恩健 刘晓娟 |
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| 作者单位： | 1. 东华大学信息科学与技术学院,上海,201620;中国科学院研究生院信息安全国家重点实验室,北京,100039
2. 上海电力学院数理系,上海,2000901 |
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| 摘 要： | 本文构造了两类Zpq上阶数为4的广义割圆序列并研究了它们的周期自相关函数,研究结果表明第一类序列具有7值自相关函数,并且当(p-1)(q-1)/16为偶数时,适当选取p,q可以使自相关函数降为6值或5值;当(p-1)(q-1)/16为奇数时,适当选取p,q可以使自相关函数降为5值.第二类序列具有5值自相关函数,并且当口q-p=4时,该序列为3值自相关序列.
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| 关 键 词： | 广义割圆数 广义割圆序列 自相关函数 |
Generalized Cyclotomic Sequences of Order Four Over Zpq and Their Autocorrelation Values |
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| BAI En-jian,LIU Xiao-juan.Generalized Cyclotomic Sequences of Order Four Over Zpq and Their Autocorrelation Values[J].Chinese Journal of Engineering Mathematics,2008,25(5). |
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| Authors: | BAI En-jian LIU Xiao-juan |
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| Abstract: | In this paper, we first introduce two kinds of generalized cyclotomic sequences of order four over Zpq, and then calculate the autocorrelation values of these sequences. The periodic autocorrelation function of the first kind of sequences is seven-valued and the second kind of sequences five-valued. If the two primes p, q are chosen properly, the autocorrelation values of the first kind of sequence can be reduced to six-value or five-value if (p - 1)(q - 1)/16 is even and five-value if (p - 1)(q - 1)/16 is odd, respectively. If q - p = 4, the second kind of sequence has the optimal autocorrelation. |
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| Keywords: | generalized cyclotomic numbers generalized cyclotomic sequences autocorrelation function |
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