Construction of Irreducible Polynomials in Galois fields, GF(2m) Using Normal Bases
Abraham Aidoo *
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
Kwasi Baah Gyam
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Irreducible polynomials, primitive polynomials, field, finite fields, order of a finite field, normal bases.