Determination of a Type of Permutation Trinomials over Finite Fields, II

Abstract

Let $q$ be a prime power. We determine all permutation trinomials of ${\mathbb{F}}_{q^2}$ of the form $ax+b{x}^q+x^{2q-1}\in {\mathbb{F}}_{q^2}[x]$. The subclass of such permutation trinomials of ${\mathbb{F}}_{q^2}$ with $a,b\in {\mathbb{F}}_q$ was determined in a recent paper by the author.

arXiv comment16 pages

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