On a conjecture about a class of permutation trinomials.

We prove a conjecture by Tu, Zeng, Li, and Helleseth concerning trinomials f α , β ( x ) = x + α x q ( q − 1 ) + 1 + β x 2 ( q − 1 ) + 1 ∈ F q 2 [ x ] , α β ≠ 0 , q even, characterizing all the pairs ( α , β ) ∈ F q 2 2 for which f α , β ( x ) is a permutation of F q 2 . [ABSTRACT FROM AUTHOR]