Construction and Determination of Irreducible Polynomials in Galois elds, GF(2m)
Abraham Aidoo, Kwasi Baah Gyam, Fengfan Yang
Journal of Advances in Mathematics and Computer Science · pp. 1–6 · Published 3 Aug 2019
10.9734/jamcs/2019/v33i330181Abstract
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 $$F_2[x]$$.
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