确定有限域上给定周期的不可约多项式的个数以及利用低次不可约多项式构造高次不可约多项式

Determining the Number of Irreducible Polynomials Over a Field of a Given Period and Constructing Irreducible Polynomials of High Degree

主要利用较文献 [4]更为简明的方法证明了有关有限域 Fq(q为一个素数幂 )上的以 l为周期的 n次不可约多项式的个数的结论 ,另外 ,本文结合初等数论知识得到了前面这个结论的几个推论 ,并对利用低次不可约多项式构造高次不可约多项式进行了研究 .

Let q be a power of a prime number and F q a finite field of q elements. In this paper, we discuss the number of irreducible polynomials over F q of degree m and period l, moreover, we describle a principle of obtaining new irreducible polynomials from known ones.