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

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.

Abstract:

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.