Construction and Determination of Irreducible Polynomials in Galois elds, GF(2m)
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.
Fengfan Yang
Department of Communication and Information System, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu Province, China.
*Author to whom correspondence should be addressed.
Abstract
This work is about Construction of Irreducible Polynomials in Finite fields. We defined some terms in the Galois field that led us to the construction of the polynomials in the GF(2m). We discussed the following in the text; irreducible polynomials, monic polynomial, primitive polynomials, eld, Galois eld or nite elds, and the order of a finite field. We found all the polynomials in $$F_2[x]$$ that is, $$P(x) =\sum_{i=1}^m a_ix^i : a_i \in F_2$$ with $$a_m \neq 0$$ for some degree $m$ which
led us to determine the number of irreducible polynomials generally at any degree in $$F_2[x]$$.
Keywords: Irreducible polynomials, field, finite fields.