The Construction and Determination of Irreducible Polynomials Over Finite Fields

摘要

The approach for constructing the irreducible polynomials of arbitrary degree n over finite fields which is based on the number of the roots over the extension field is presented. At the same time, this paper includes a sample to illustrate the specific construction procedures. Then in terms of the relationship between the order of a polynomial over finite fields and the order of the multiplicative group of the extension field, a method which can determine whether a polynomial over finite fields is irreducible or not is proposed. By applying the Euclidean Algorithm, this judgment can be verified easily.