两类广义分圆序列的自相关值  

Autocorrelation values of two classes of generalized cyclotomic sequences

作　　者：王艳[1] 韩西林 闫联陶 相乃姣 WANG Yan;HAN Xilin;YAN Liantao;XIANG Naijiao(School of Science,Xi’an University of Architecture and Technology,Xi’an Shaanxi 710055)

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《首都师范大学学报（自然科学版）》2023年第6期1-7,共7页Journal of Capital Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(61902304)。

摘　　要：基于广义分圆理论,构造了一类周期为2p的二元广义分圆序列和一类周期为pq的二元广义分圆序列,利用分圆数和差集理论讨论了这2类序列的自相关函数值。对于周期为2p的二元广义分圆序列,当p≡1(mod8)时,该类序列具有几乎最优的自相关函数值;当p≡3(mod8)时,该类序列的自相关函数值是四值。对于周期为pq的二元广义分圆序列,当(p-1)(q-1)/4是偶数时,该类序列具有几乎最优的自相关函数值;当(p-1)(q-1)/4是奇数时,该类序列的自相关函数值为四值。结果表明,构造的2类二元广义分圆序列都具有低值自相关性质。A class of generalized cyclotomic binary sequences with period 2p and a class of generalized cyclotomic binary sequences with periods pq are constructed based on generalized cyclotomic theory.The autocorrelation values of two classes of generalized cyclotomic binary sequences with periods 2p and pq are determined by cyclotomic number and different sets.The class of binary sequences with period 2p have almost optimal autocorrelation function values when p≡1(mod8)and 4-value autocorrelation when p≡3(mod8).The class of binary sequences with periods pq have almost optimal autocorrelation function values when(p-1)(q-1)/4 is even and 4-value autocorrelation when(p-1)(q-1)/4 is odd.Results show that the class of sequences with periods pq and 2p in this paper have low-value autocorrelation.

关 键 词：流密码 自相关性 分圆 伪随机序列 

分 类 号：TN918.4[电子电信—通信与信息系统]