两类具有低自相关和大线性复杂度的4p周期二元序列  

TWO CLASSES OF BINARY SEQUENCES OF PERIOD 4p WITH LOW AUTOCORRELATION AND LARGE LINEAR COMPLEXITY

作　　者：杨波[1] 朱自坤 肖自碧[1] YANG Bo;ZHU Zi-kun;XIAO Zi-bi(College of Science,Wuhan University of Science and Technology,Wuhan 430065,China)

机构地区：[1]武汉科技大学理学院,湖北武汉430065

出　　处：《数学杂志》2024年第1期17-34,共18页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(12061027).

摘　　要：具有良好自相关性质和大线性复杂度的二元序列设计对于通信系统和流密码的各种应用非常重要.本文从Hall六次剩余序列和它们的修改版本中选取4条合适的序列作为基序列,利用交织技术构造了两类周期为4p的二元序列,并且完全确定了这两类序列的自相关和线性复杂度.研究结果表明这两类序列既具有低自相关性质又具有非常大的线性复杂度.The design of binary sequences with good autocorrelation property and large linear complexity is very important for diverse applications of communication systems and stream ciphers.In this paper,we propose two classes of binary sequences of period 4p constructed by interleaving four appropriate sequences chosen from Hall's sextic residue sequences and their modi¯ed versions.The autocorrelation and linear complexity of these sequences are completely determined.The results show that the proposed sequences have both low autocorrelation sidelobes as well as very large linear complexity.

关 键 词：二元序列 交织结构 自相关 线性复杂度 

分 类 号：O157.4[理学—数学]