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 (6)

• Several Classes of Permutation Trinomials From Niho Exponents
• A Class of Binomial Permutation Polynomials
• Permutation polynomials on F_q induced from bijective Redei functions on subgroups of the multiplicative group of F_q
• New Permutation Trinomials Constructed from Fractional Polynomials
• New Permutation Trinomials From Niho Exponents over Finite Fields with Even Characteristic
• New Classes of Permutation Binomials and Permutation Trinomials over Finite Fields

Cited by in corpus (1)

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