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Motivated by recent results on the constructions of permutation polynomials with few terms over the finite field $mathbb{F}_{2^n}$, where $n$ is a positive even integer, we focus on the construction of permutation trinomials over $mathbb{F}_{2^n}$ from Niho exponents. As a consequence, several new classes of permutation trinomials over $mathbb{F}_{2^n}$ are constructed from Niho exponents based on some subtle manipulation of solving equations with low degrees over finite fields.
In this paper, a class of permutation trinomials of Niho type over finite fields with even characteristic is further investigated. New permutation trinomials from Niho exponents are obtained from linear fractional polynomials over finite fields, and
Let $mathbb{F}_{p^{n}}$ be the finite field with $p^n$ elements and $operatorname{Tr}(cdot)$ be the trace function from $mathbb{F}_{p^{n}}$ to $mathbb{F}_{p}$, where $p$ is a prime and $n$ is an integer. Inspired by the works of Mesnager (IEEE Trans.
Let $mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with their stud
In this paper, let $n=2m$ and $d=3^{m+1}-2$ with $mgeq2$ and $gcd(d,3^n-1)=1$. By studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over the finite field $mathbb{F}_{3^n}$, the cor
Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation polynomials