On Permutation Trinomials of the type $X^{q^2-q+1}+AX^{q^2}+BX$ over $\mathbb{F}_{q^3}$ (2306.09972v1)

Abstract: Necessary and sufficient conditions on $A,B\in \mathbb{F}{q^3}^*$ for $f(X)=X^{q^2-q+1}+AX^{q^2}+BX$ being a permutation polynomial of $\mathbb{F}{q^3}$ are investigated via a connection with algebraic varieties over finite fields.