Correction to: Some classes of permutation polynomials of the form $b(x^q+ax+\delta )^{\frac{i(q^2-1)}{d}+1}+c(x^q+ax+\delta )^{\frac{j(q^2-1)}{d}+1}+L(x)$ over $\mathbb{F}_{q^2}$

1 Correction to: Applicable Algebra in Engineering, Communication and Computing https://doi.org/10.1007/s00200-020-00441-z

In the original publication of the article, the mathematics symbol $q$ was replaced with “s” by mistake while replacing the math mode to text mode. As a result, the first sentence in the following sections are affected and correct sentences should read as given below:

Abstract

Let $q$ be a prime power and ${\mathbb{F}}_q$ be a finite field with $q$ elements.

2 Introduction

Let ${\mathbb{F}}_q$ be the finite field with $q$ elements, where $q$ is a prime power, and let ${\mathbb{F}}_q[x]$ be the ring of polynomials of one variable over ${\mathbb{F}}_q$.

Lemma 2

(See [26]) For a prime power $q$, assume that $a \in {\mathbb{F}}_{q^2}$ with $a^{q+1}=1$ and $g\in {\mathbb{F}}_{q^2}$ is a primitive element of ${\mathbb{F}}_{q^2}$.

Theorem 1

For a prime power $q$ and positive integers $d, i,j$ with $q\equiv1 \pmod{d}$, assume that $b,c \in {\mathbb{F}}_q$ and $a, \delta \in {\mathbb{F}}_{q^2}$ with $a^{1+q}=1$.

Theorem 2

For a prime power $q$ and positive integers $d, i,j$ with $q\equiv1 \pmod{d}$, assume that $b,c \in {\mathbb{F}}_q$, $a \in {\mathbb{F}}_{q^2}$ with $a^{1+q}=1$, and $g \in {\mathbb{F}}_{q^2}$ is a primitive element of ${\mathbb{F}}_{q^2}$.

Theorem 3

For a prime power $q$ and positive integers $d, i,j, s, k$ with $q\equiv-1 \pmod{d}$, $iq\equiv s \pmod{d}$ and $jq\equiv k \pmod{d}$, assume that $b,c \in {\mathbb{F}}_q$ and $a, \delta \in {\mathbb{F}}_{q^2}$ satisfying $a^{1+q}=1$.

The original article has been updated accordingly.