摘要
设正整数n(≥2),N={α_i|i=0,1,…,n-1)是有限域F_(2n)在F_2的正规基,且t_i=Tr(αα_i)(i=0,1,…,n-1),其中Tr(α)是α∈F_(2n)在F_2上的迹映射.本文讨论了F_(2n)在F_2上的满足如下条件的高斯正规基的存在性:t_0=t_1=t_(n-1),t_i=0(i≠0,1,n-1).给出了这种正规基的对偶基,并由此确定了F_(2n)在F_2上满足上述条件的全部最优正规基.
Let n(≥2)be an integer,N={α_i|i=0,1,…,n-1} be a normal basis of F_(2n)over F_2,and t_i=Tr(ααi)(i=0,1,…,n-1),where Tr(α)denotes the trace mapping ofα∈F_(2n)over F_2.In this paper,we discuss the existence of Gauss period normal bases,satisfying t_0=t_1=t_(n-1)and others equal to 0,of F_(2n) over F_2.We also obtain the dual for these normal bases and then determine all optimal normal bases of F_(2n) over F_2 satisfying the above condition.
出处
《数学进展》
CSCD
北大核心
2015年第3期394-404,共11页
Advances in Mathematics（China）
基金
The second author is supported by NSFC(No.11401408)
Sichuan Provincial Foundation of China(No.14ZA0034)
Sichuan Normal University Key Project Foundation(No.13ZDL06)
关键词
有限域
正规基
对偶基
迹映射
finite field
normal basis
dual basis
trace mapping
