A revisit to a class of permutation quadrinomials

Abstract

This paper revisits the quadrinomials x3q+a1x2q+1+a2xq+2+a3x3 over Fq2, where q is a power of 2. We propose a more comprehensive characterization of the coefficients that give rise to new permutation quadrinomials. The new characterization not only contains those coefficients given in [20], but also seems to completely cover all the coefficients that yield permutation quadrinomials, which is evidenced by exhaustive searches on small finite fields.