偶特征有限域上一类正规基及其对偶基(英文)  

A Class of Special Normal Bases and Their Dual Bases Over Finite Fields With Even Characteristic

作　　者：李波[1] 廖群英[2] 

机构地区：[1]重庆邮电大学移通学院,重庆401520 [2]四川师范大学数学与软件科学学院,成都四川610066

出　　处：《数学进展》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)

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.

关 键 词：有限域 正规基 对偶基 迹映射 

分 类 号：O156[理学—数学]