The compositional inverses of linearized permutation binomials over finite fields

Abstract

Let $q$ be a prime power and $n$ and $r$ be positive integers. It is well known that the linearized binomial $L_r(x)=x^{q^r}+ax\in {\mathbb{F}}_{q^n}[x]$ is a permutation polynomial if and only if $(-1{)}^{n/d}{a}^{(q^n-1)/(q^d-1)}\ne 1$ where $d=(n,r)$. In this paper, the compositional inverse of $L_r(x)$ is explicitly determined when this condition holds.

References in corpus (1)

• The compositional inverse of a class of linearized permutation polynomials over ${\mathbb{F}}_{2^n}$, $n$ odd

Cited by in corpus (3)

• On inverses of some permutation polynomials over finite fields of characteristic three
• Compositional inverses, complete mappings, orthogonal Latin squares and bent functions
• Several classes of bent, near-bent and 2-plateaued functions over finite fields of odd characteristic