有限域上的(4,7)型高斯正规基及其对偶基和迹基
The dual and trace bases of the type (4,7) Gauss normal basis over finite fields
作者：魏杰(四川师范大学数学与软件科学学院)；李雪连(四川师范大学数学与软件科学学院)；廖群英(四川师范大学数学与软件科学学院)
Author：WEI Jie(Institute of Mathematics and Software Science, Sichuan Normal University)；LI Xue-Lian(Institute of Mathematics and Software Science, Sichuan Normal University)；LIAO Qun-Ying(Institute of Mathematics and Software Science, Sichuan Normal University)
收稿日期：2015-04-22 年卷（期）页码：2016,53(1):7-12
期刊名称：四川大学学报: 自然科学版
Journal Name：Journal of Sichuan University (Natural Science Edition)
关键字：有限域, 高斯正规基, 对偶基, 迹正规基,乘法表, 复杂度
Key words：Finite field, Gauss period normal basis, Dual basis, Trace normal basis, Multiplication table, Complexity
基金项目：
中文摘要
设q是素数p的方幂,最近文[8]通过刻画有限域上分圆数的性质,给出了有限域上一类高斯正规基复杂度的准确计算公式.并且,证明了Fqn 在Fq 的7-型高斯正规基满足所给的条件当且仅当n≠4. 本文完善了上述结果,确定了有限域 Fq4 在 有限域 Fq 上的7-型高斯正规基及其对偶基和迹基的准确复杂度.
英文摘要
Let q be a power of the prime p and let Fqbe the finite field with q elements.Recently, by characterizing some properties of cyclotomic numbers, they obtain the explicit formula for the complexity of a class of Gauss period normal bases over finite fields.Furthermore, they show that the type 7 Gauss period normal basis of Fqn over Fq is just the desired basis except for n = 4. In this paper, we compete this result and obtain the explicit formula for the complexity of 7 type Gauss period normal bases of Fq4 over Fq.
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