Irreducible polynomials over \(\mathrm{GF}(2)\) with three prescribed coefficients. (Q1400975)

The authors give formulas for the number of irreducible polynomials \[ p(x)=x^n+a_1x^{n-1}+ a_2x^{n-2}+a_3x^{n-3}+\ldots+a_{n-1}x+a_n\in\mathbb{F}_2[x] \] of an odd degree \(n\) in which the coefficients \(a_1\), \(a_2\), and \(a_3\) are given. Their enumeration is based on computations with quadratic forms over \(\mathbb{F}_2\). The case of even \(n\) is discussed by \textit{J. L. Yucas} and \textit{G. L. Mullen} [Discrete Math. 274, 265--279 (2004; Zbl 1039.11090)].