Generalized cyclotomic mappings: Switching between polynomial, cyclotomic, and wreath product form

2021/03/01 by Alexander Bors, Qiang Wang, Bors, Alexander +1 · 1 citation
Computer Science · Mathematics · #11T06 #20E22 #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary 11T22. Secondary 11A07

paper · pdf · doi:10.48550/arxiv.2103.00664

openalex publication_date 2021/03/01 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with so-called index d generalized cyclotomic mappings of a finite field \mathbbF_q, which are functions \mathbbF_q→\mathbbF_q that agree with a suitable monomial function x↦ ax^r on each coset of the index d subgroup of \mathbbF_q^∗. We discuss two important rewriting procedures in the context of generalized cyclotomic mappings and present applications thereof that concern index d generalized cyclotomic permutations of \mathbbF_q and pertain to cycle structures, the classification of (q-1)-cycles and involutions, as well as inversion.

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