通信学报 ›› 2019, Vol. 40 ›› Issue (2): 197-206.doi: 10.11959/j.issn.1000-436x.2019034

• 学术通信 • 上一篇    

关于二元割圆序列的k-错线性复杂度

陈智雄1,吴晨煌1,2()   

  1. 1 莆田学院福建省高校应用数学重点实验室,福建 莆田 351100
    2 电子科技大学计算机科学与工程学院,四川 成都 611731
  • 修回日期:2019-01-17 出版日期:2019-02-01 发布日期:2019-03-04
  • 作者简介:陈智雄(1972– ),男,福建莆田人,博士,莆田学院教授,主要研究方向为序列密码。|吴晨煌(1981– ),男,福建莆田人,莆田学院副教授,电子科技大学博士生,主要研究方向为序列密码。
  • 基金资助:
    国家自然科学基金资助项目(61772292);国家自然科学基金国际合作交流基金资助项目(6181101289);福建省自然科学基金资助项目(2018J01425);福建省高校创新团队培育计划基金资助项目(2018-49)

k-error linear complexity of binary cyclotomic generators

Zhixiong CHEN1,Chenhuang WU1,2()   

  1. 1 Provincial Key Laboratory of Applied Mathematics,Putian University,Putian 351100,China
    2 School of Computer Science and Engineering,University of Electronic Science and Technology of China,Chengdu 611731,China
  • Revised:2019-01-17 Online:2019-02-01 Published:2019-03-04
  • Supported by:
    The National Natural Science Foundation of China(61772292);Projects of International Cooperation and Exchanges NSFC(6181101289);The Natural Science Foundation of Fujian Province(2018J01425);Program for Innovative Research Team in Science and Technology in Fujian Province University(2018-49)

摘要:

应用伪随机序列的离散傅里叶变换,讨论了周期为素数p的Legendre序列、Ding-Helleseth-Lam 序列及Hall六次剩余序列的k-错线性复杂度。具体地,首先确定了上述3种序列的1-错线性复杂度,其次对k≥2,以及2模p的阶的一些特殊取值,讨论了相应序列的k-错线性复杂度。

关键词: Legendre序列, Ding-Helleseth-Lam序列, Hall六次剩余序列, k-错线性复杂度, 离散傅里叶变换

Abstract:

In terms of the discrete Fourier transforms,the k-error linear complexities over F2were discussed for Legendre,Ding-Helleseth-Lam,and Hall's sextic residue sequences of odd prime period p.More precisely,the 1-error linear complexities of these sequences were determined.Then,with some special restrictions of the order of 2 modulo p,partial results on their k-error linear complexities (k≥2) were proved.

Key words: Legendre sequence, Ding-Helleseth-Lam sequence, Hall's sextic residue sequence, k-error linear complexity, discrete Fourier transform

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