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-wiseFp-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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
