Permutation polynomials over \mathbbF_q² from rational functions

2018/02/14 by Daniele Bartoli, Bartoli, Daniele, Ariane M. Masuda +3
Computer Science · Mathematics · #05A05 #11T06 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05A05 #msc:11T06

paper · pdf · doi:10.48550/arxiv.1802.05260

arxiv created 2018/02/14 · openalex publication_date 2018/02/14 · arxiv updated 2018/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let μ_q+1 denote the set of (q+1)-th roots of unity in \mathbbF_q² . We construct permutation polynomials over \mathbbF_q² by using rational functions of any degree that induce bijections either on μ_q+1 or between μ_q+1 and \mathbbF_q ∪ \∞\. In particular, we generalize results from Zieve.

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