Some observations on bent and planar functions
Combinatorics
2025-11-25 v1
Abstract
We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd characteristic via their equivalence to perfect non-linear functions in that setting. We end by demonstrating, by entirely elementary means, that the distance between two distinct planar functions must be at least two.
Cite
@article{arxiv.2511.17815,
title = {Some observations on bent and planar functions},
author = {Robert S. Coulter and Steven Senger},
journal= {arXiv preprint arXiv:2511.17815},
year = {2025}
}