给定k-错非线性复杂度的有限长二元序列的分布  

The Distribution of Finite-Length Binary Sequences with Given k-Error Nonlinear Complexity

作　　者：孙志敏 曾祥勇 许雪莹 陈智雄[3] SUN Zhi-Min;ZENG Xiang-Yong;XU Xue-Ying;CHEN Zhi-Xiong(Hubei Key Laboratory of Applied Mathematics,School of Cyber Science and Technology,Hubei University,Wuhan 430062,China;Hubei Key Laboratory of Applied Mathematics,Faculty of Mathematics and Statistics,Hubei University,Wuhan 430062,China;Fujian Key Laboratory of Financial Information Processing,Putian University,Putian 351100,China)

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：《密码学报（中英文）》2024年第2期466-484,共19页Journal of Cryptologic Research

基　　金：国家自然科学基金(62072161);湖北省科技厅创新群体(2003AFA021);福建省自然科学基金(2023J01996);福建省金融信息处理重点实验室(莆田学院)(JXC202206)。

摘　　要：当n<2c且具有相同k-错非线性复杂度时,本文证明了长度为n非线性复杂度为c的二元序列与长度为n+t非线性复杂度为c+t的二元序列有相同的数目(t为任意非负整数);对于长度为n非线性复杂度为c的二元序列,确定了k-错非线性复杂度分别为1和2的序列数目.When n<2c and the k-error nonlinear complexity is fixed,this paper proves that the number of sequences with length n and nonlinear complexity c is the same as that of the sequences with length n+t and nonlinear complexity c+t(t is any nonnegative integer).For binary sequences with length n and nonlinear complexity c,the numbers of such sequences with k-error nonlinear complexity 1 and 2 can be precisely determined.

关 键 词：k-错非线性复杂度 非线性复杂度 有限长序列 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]