Construction and Determination of Irreducible Polynomials in Galois elds, GF(2m)

This work is about Construction of Irreducible Polynomials in Finite elds. We de ned someterms in the Galois eld that led us to the construction of the polynomials in theGF(2m).We discussed the following in the text; irreducible polynomials, monic polynomial, primitivepolynomials, eld, Galois eld or nite elds, and the order of a nite eld. We found all thepolynomials inF2[x] that is,P(x) =∑mi=1aixi:ai∈F2witham̸= 0 for some degreemwhichled us to determine the number of irreducible polynomials generally at any degree inF2[x].