On permutation trinomials of type $x^{2p^s+r}+x^{p^s+r}+\lambda x^r$

Abstract

We determine all permutation trinomials of type $x^{2p^s+r}+x^{p^s+r}+\lambda x^r$ over the finite field ${\mathbb{F}}_{p^t}$ when $(2p^s+r{)}^4<p^t$. This partially extends a previous result by Bhattacharya and Sarkar in the case $p=2$, $r=1$.