Some results about permutation properties of a kind of binomials over finite fields

2019/06/21 by Xiaogang Liu, Liu, Xiaogang
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1906.09168

openalex publication_date 2019/06/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

Permutation polynomials have many applications in finite fields theory, coding theory, cryptography, combinatorial design, communication theory, and so on. Permutation binomials of the form x^r(x^q-1+a) over \mathbbF_q² have been studied before, K. Li, L. Qu and X. Chen proved that they are permutation polynomials if and only if r=1 and a^q+1\not=1. In this paper, we consider the same binomial, but over finite fields \mathbbF_q³ and \mathbbF_q^e. Two different kinds of methods are employed, and some partial results are obtained for them.

Citations

• Permutation polynomials and group permutation polynomials

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