有限域上的(4,7)型高斯正规基及其对偶基和迹基

Dual and trace bases of the type(4,7) Gauss period normal basis over finite fields

设q为素数p的n次方幂,n为正整数.最近廖和胡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,并证明了有限域Fqn在Fq上的7-型高斯正规基满足所给条件当且仅当n≠4.本文完善了上述结果,确定了Fq4在Fq上的7-型高斯正规基及其对偶基和迹基的准确复杂度.

Let q be a power of the prime p and Fq be the finite field with q elements. Recently, by characterizing some properties of eyelotomic numbers, Liao and Li obtained the explicit formula for the complexity of a class of Gauss period normal bases over finite fields. Furthermore, they showed that the type 7 -Gauss period normal basis of Fqn over fq is just the desired basis except for n = 4, her n is an integer. In this paper, we complete the above results and obtain the explicit formula for the complexity of type 7 -Gauss period basis of Fq4 over Fq .