Construction of Irreducible Polynomials in Galois elds, GF(2m) Using Normal Bases

This thesis is about Construction of Polynomials in Galois fields Using Normal Bases in finite fields. In this piece of work, we discussed the following in the text; irreducible polynomials, primitive polynomials, field, Galois field or finite fields, and the order of a finite field. We found the actual construction of polynomials in GF(2m) with degree less than or equal to m − 1 and also illustrated how this construction can be done using normal bases. Finally, we found the general rule for construction of GF(pm) using normal bases and even the rule for producing reducible polynomials.