具有极大非线性复杂度的有限长二元序列的k-错非线性复杂度  

k-Error Nonlinear Complexity of Finite-Length Binary Sequences with Large Nonlinear Complexity

作　　者：孙志敏 曾祥勇 梁思诚 陈智雄[3] SUN Zhimin;ZENG Xiangyong;LIANG Sicheng;CHEN Zhixiong(Hubei Key Laboratory of Applied Mathematics,School of Cyber Science and Technology,Hubei University,Wuhan 430062;Faculty of Mathematics and Statistics,Hubei Key Laboratory of Applied Mathematics,Hubei University,Wuhan 430062;Fujian Key Laboratory of Financial Information Processing,Putian University,Putian 351100)

机构地区：[1]湖北大学网络空间安全学院,湖北省应用数学重点实验室,武汉430062 [2]湖北大学数学与统计学学院,湖北省应用数学重点实验室,武汉430062 [3]莆田学院,福建省金融信息处理重点实验室,莆田351100

出　　处：《系统科学与数学》2023年第10期2693-2713,共21页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(62072161);福建省金融信息处理重点实验室(莆田学院)(JXC202206)资助课题。

摘　　要：k-错非线性复杂度是用来度量序列非线性复杂度稳定性的一个重要指标.对具有极大非线性复杂度的有限长二元序列,完全确定了k-错非线性复杂度为0的序列数目,给出了k-错非线性复杂度为1的序列数目下界.此外,得到了k-错非线性复杂度不超过某个给定值的序列数目下界.The k-error nonlinear complexity is a measure to assess the stability of nonlinear complexity of a sequence.For finite-length binary sequences with large nonlinear complexity,we determine the exact number of sequences having k-error nonlinear complexity 0,and present a lower bound on the number of sequences having k-error nonlinear complexity 1.Furthermore,we get a lower bound on the number of these sequences having k-error nonlinear complexity no more than a positive integer.

关 键 词：二元序列 非线性复杂度 k-错非线性复杂度 

分 类 号：TN918.1[电子电信—通信与信息系统]