有限域上分圆多项式

Cyclotomic polynomials over finite fields

探讨有限域上分圆多项式的计算性质,并给出有限域上分圆多项式不可约的条件,最后,给出由分圆多项式求有限域上给定次数的所有不可约多项式。为有限域上不可约多项式理论的完善和应用提供一些理论依据。

In this paper, Some calculation features on eyclotomie polynomials over finite fields have been discussed, and then the conditions of irreducibility about cyclotomic polynomials have been given. Finally, for a given positive integral , Calcula- tion all the irreducible polynomials with given degree over finite fields by cyclotomic polynomials has been solved. These re- suits provided some evidence on theory and applications of irreducible polynomials over finite fields.