On the construction of irreducible self-reciprocal polynomials over finite fields

Abstract

The transformation f(x){mapping}fQx{colon equals}deg(f)f(x + 1/x) for f(x)∈ {Mathematical expression} is studied. Simple criteria are given for the case that the irreducibility of f is inherited by the self-reciprocal polynomial fQ. Infinite sequences of irreducible self-reciprocal polynomials are constructed by iteration of this Q-transformation. © 1990 Springer-Verlag.