A family of permutation trinomials in ${\mathbb{F}}_{q^2}$

Abstract

Let $p>3$ and consider a prime power $q=p^h$. We completely characterize permutation polynomials of ${\mathbb{F}}_{q^2}$ of the type $f_{a,b}(X)=X(1+a{X}^{q(q-1)}+b{X}^{2(q-1)})\in {\mathbb{F}}_{q^2}[X]$. In particular, using connections with algebraic curves over finite fields, we show that the already known sufficient conditions are also necessary.

References in corpus (1)

• Several Classes of Permutation Trinomials From Niho Exponents