Paper Info
Title
Coset-wise affine functions and cycle types of complete mappings
Abstract
Let K be a finite field of characteristic p. We study a certain class of functions K→K that agree with an Fp-affine function K→K on each coset of a given additive subgroup W of K – we call them W-coset-wise Fp-affine functions of K. We show that these functions form a permutation group on K with the structure of an imprimitive wreath product and characterize which of them are complete mappings of K. As a consequence, we are able to provide various new examples of cycle types of complete mappings of K – for instance, if p>2, then all cycle types where each cycle has length a power of p are achieved by complete mappings of K.
Year
DOI
Venue
2022
10.1016/j.ffa.2022.102088
Finite Fields and Their Applications
Keywords
DocType
Volume
primary,secondary
Journal
83
ISSN
Citations 
PageRank 
1071-5797
0
0.34
References 
Authors
0
2
Name
Order
Citations
PageRank
Alexander Bors100.34
Qiang Wang223737.93