On Two Conjectures about Permutation Trinomials over ${\mathbb{F}}_{3^{2k}}$

Abstract

Permutation polynomials with few terms attracts researchers' interest in recent years due to their simple algebraic form and some additional extraordinary properties. In this paper, by analyzing the quadratic factors of a fifth-degree polynomial and a seventh-degree polynomial over the finite field ${\mathbb{F}}_{3^{2k}}$, two conjectures on permutation trinomials over ${\mathbb{F}}_{3^{2k}}$ proposed recently by Li, Qu, Li and Fu are settled, where $k$ is a positive integer.

References in corpus (1)

• Several Classes of Permutation Trinomials From Niho Exponents

Cited by in corpus (1)

• Several Classes of Permutation Trinomials over ${\mathbb{F}}_{5^n}$ From Niho Exponents