摘要
对于将有限域上的自对偶基概念推广到了更一般的弱自对偶的情形,给出了有限域上存在这类正规基的一个充妥条件:设q为素数幂,E=Fqn为q元域F=Fq的n次扩张,N={αi=αqi|i=0,1,…,n-1}为E在F上的一组正规基．则存在c∈F*及r,0≤r≤n-1,使得β=cαr生成N的对偶基的充要条件是以下三者之一成立: (1)q为偶数且n≠0(mod 4);(2) n与q均为奇数;(3)q为奇数,n为偶数,(-1)为F中的非平方元且r为奇数．
This paper expands self-dual bases to general weakly self-dual bases and gets a sufficient and necessary condition for the finite field which has a weakly self-dual normal basis as the following： Let q be the power of a prime, E = Fq^n be the n-dimensional extension of the finite field F = Fq, and N = {αi = α^q^i ｜ i = 0, 1,... , n - 1} be a normal basis of E over F. Then there exist some c ∈ F^＊ and some r, 0 ≤ r ≤n - 1 such that β = cαr generates the dual of N if and only if either q is even and n ≠ 0 （mod 4）; or n and q are odd; or q is odd, n is even, （-1） is a nonsquare in F and r is odd.
出处
《数学年刊（A辑）》
CSCD
北大核心
2007年第2期273-280,共8页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10671137)
博士点科研专项基金(No.20060636001)
四川省教育厅青年基金(No.2005B024)资助的项目
关键词
有限域
正规基
对偶基
迹
复杂度
Finite fields, Normal bases, Self-dual bases, Trace function,Complexity
