A Note on Trace Representation of Legendre Sequences

DU Xiao-ni; CHEN Zhi-xiong

您当前的位置：

首页 >

文章列表页 >

A Note on Trace Representation of Legendre Sequences

更新时间：2025-07-16

- A Note on Trace Representation of Legendre Sequences
- Acta Electronica Sinica Vol. 39, Issue 4, Pages: 869-871(2011)
- 作者机构：
  
  1. 西北师范大学数学与信息科学学院,甘肃,兰州,730070
  2. 中国科学院研究生院信息安全国家重点实验室,北京,100049
  3. 莆田学院应用数学重点实验室,福建,莆田,351100
  4. 西北师范大学数学与信息科学学院甘肃兰州,730070
  5. 中国科学院研究生院信息安全国家重点实验室北京,100049
  6. 莆田学院应用数学重点实验室福建莆田,351100
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.4
- Published：2011
- 稿件说明：
移动端阅览
DU Xiao-ni, CHEN Zhi-xiong. A Note on Trace Representation of Legendre Sequences[J]. Acta Electronica Sinica, 2011, 39(4): 869-871.
DOI：

DU Xiao-ni, CHEN Zhi-xiong. A Note on Trace Representation of Legendre Sequences[J]. Acta Electronica Sinica, 2011, 39(4): 869-871. DOI：

摘要

当素数

≡3或-3(mod 8)时

Kim等利用有限域GF(2

) 中两个不同的本原元刻画了周期为

的Legendre序列的迹表示.本文通过分割有限域的乘法群GF(

)

关于元素4生成的子群的陪集

利用从GF(2

)到子域GF(4)的迹函数

提出Legendre序列的一种新的迹表示形式.该结论仅用GF(2

)中的一个本原元即可确定序列

对其计算实现有积极的意义.

Abstract

Kim et al.determined the trace function representation of Legendre sequences with prime period

≡3 or -3 (mod 8) by using two different primitive elements of the finite field GF(2^

).In this correspondence

firstly

the authors divide the group GF(

)

into the union of cosets of subgroup generated by 4.Then

they propose a new trace function representation of Legendre sequences via the trace function from the finite field GF(2^

) to its subfield GF(4).The trace representation is described only using one primitive element of the finite field GF(2^

).It has positive effect to the computational implementation of Legendre sequences.

关键词

Keywords

references

Views

964

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

The 4-Error Linear Complexity of Binary Periodic Sequences

The Linear Complexity of the Generalized Self-Shrinking Generator on GF(q)

A Relationship Between Autocorrelation and Linear Complexity

A Fast Method for Constructing GMW Sequences with Largest Linear Spans

On the k-Error Linear Complexity of Binary Period Sequences

Related Author

QI Wen-feng

PI Fei

WANG Jin-ling

WANG Hui-juan

LI Xue-lian

HU Yu-pu

GAO Jun-tao

XU Cheng-qian

Related Institution

State Key Laboratory of Information SecurityChinese Academy of SciencesBeijing 100190China

Department of Applied MathematicsInformation Engineering InstituteInformation Engineering UniversityZhengzhouHenan 450002China

State Key Laboratory of Information Security,Chinese Academy of Sciences

Department of Applied Mathematics,Information Engineering Institute,Information Engineering University

Mathematics Department, Zhengzhou University

⁰