A short note on permutation trinomials of prescribed type
Yıldırım Akbal, Burcu Gülmez Temür, Pınar Ongan · Communications in Algebra · 2019
We show that there are no permutation trinomials of the form h(x)=x5(x5(q−1)+xq−1+1) over Fq2 where q is not a power of 2. Together with a result of Zha, Z., Hu, L., Fan, S., h(x) permutes Fq2 if q=2k where k≡2 (mod 4), this gives a complete classification of those q’s such that h(x) permutes Fq2.