Constructive problems for irreducible polynomials over finite fields
Proceedings of the third Canadian workshop on Information theory and applications
Tests and constructions of irreducible polynomials over finite fields
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
Self-Reciprocal Irreducible Polynomials Over Finite Fields
Designs, Codes and Cryptography
On the Number of Trace-One Elements in Polynomial Bases for $$\mathbb{F}_{2^n}$$
Designs, Codes and Cryptography
The trace spectra of polynomial bases for $${\mathbb{F}}_{2^{n}}$$
Applicable Algebra in Engineering, Communication and Computing
Finite Fields and Their Applications
Swan's theorem for binary tetranomials
Finite Fields and Their Applications
Swan-like results for binomials and trinomials over finite fields of odd characteristic
Designs, Codes and Cryptography
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Stickelberger---Swan Theorem is an important tool for determining parity of the number of irreducible factors of a given polynomial. Based on this theorem, we prove in this note that every affine polynomial A(x) over $${\mathbb{F}_2}$$ with degree 1, where A(x) = L(x) + 1 and $${L(x)=\sum_{i=0}^{n}{x^{2^i}}}$$ is a linearized polynomial over $${\mathbb{F}_2}$$ , is reducible except x 2 + x + 1 and x 4 + x + 1. We also give some explicit factors of some special affine pentanomials over $${\mathbb{F}_2}$$ .