Irreducible compositions of polynomials over finite fields of even characteristic (Q1928790)

Given a monic irreducible polynomial \(P\in\mathbb{F}_{2^s}[x]\) of degree \(n\), the authors study conditions under which \[ H(a,d)^{-1}(dx^2+rx+h)^nP\left(\frac{ax^2+bx+c}{dx^2+rx+h}\right) \] is also an irreducible polynomial, where \(ax^2+bx+c,dx^2+rx+h\in\mathbb{F}_{2^s}[x]\) are coprime with \((a,d)\not=(0,0)\) and \(H(a,d)\in\mathbb{F}_{2^s}^*\).