Binary Sequences Derived from Dickson Permutation Polynomials over Binary Extension Field

被引：0
|
作者：
Wang Hongyu [1 ]
Zheng Qunxiong [1 ,2 ]
Wang Zhongxiao [1 ]
Qi Wenfeng [1 ]
机构：
[1] PLA Strateg Support Force Informat Engn Univ, Zhengzhou 450001, Peoples R China
[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing 100093, Peoples R China
来源：
CHINESE JOURNAL OF ELECTRONICS | 2021年 / 30卷 / 03期
基金：
中国博士后科学基金; 中国国家自然科学基金;
关键词：
Permutation polynomial; Dickson polynomial; Periodicity; Shift-equivalence; Coordinate sequence; FINITE-FIELDS; CYCLE STRUCTURE; TRINOMIALS;
D O I：
10.1049/cje.2021.04.006
中图分类号：
TM [电工技术]; TN [电子技术、通信技术];
学科分类号：
0808 ; 0809 ;
摘要：
In this paper, based on a result of Lidl and Mullen (Mathematical Journal of Okayama University, 1991), the maximum length and the second maximum length that can be attained by cycles of Dickson permutation polynomial (of the first kind) with parameter 1 are studied. Necessary and sufficient conditions for these two lengths to be attained are given, which are connected with Fermat primes and Mersenne primes, respectively. Furthermore, a class of coordinate sequences that maintains a large period is obtained, which is shown to be the coordinate sequences derived from cycles of the second maximum length. Explicit formulas for their periodicity and shiftequivalences are also presented.
引用
收藏
页码：523 / 533
页数：11
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