The compositional inverses of linearized permutation binomials over finite fields

2013/11/09 by Baofeng Wu, Wu, Baofeng · 2 citations
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Wireless Communication Networks Research

paper · pdf · doi:10.48550/arxiv.1311.2154

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^qr+ax∈\mathbbF_qⁿ[x] is a permutation polynomial if and only if (-1)^n/da^(qⁿ-1)/(q^d-1)≠ 1 where d=(n,r). In this paper, the compositional inverse of L_r(x) is explicitly determined when this condition holds.

Cited by

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

Related

• The compositional inverse of a class of linearized permutation polynomials over \mathbbF_2ⁿ, n odd
• The compositional inverses of three classes of permutation polynomials over finite fields
• On the inverses of some classes of permutations of finite fields
• Linear Permutations and their Compositional Inverses over \mathbbF_qⁿ
• Permutation polynomials from a linearized decomposition