On planar functions over $\mathbb{F}_{q^3}$
Number Theory
2026-05-27 v1 Combinatorics
Abstract
Let denote the finite field of order . For odd, we investigate the planarity over of the family Using results from the theory of q-polynomials, we establish conditions under which these polynomials are planar functions. In particular, we provide characterizations for the planarity property and present new families of planar trinomials, quadrinomials, and pentanomials.
Cite
@article{arxiv.2605.26263,
title = {On planar functions over $\mathbb{F}_{q^3}$},
author = {João Paulo Guardieiro and Adler Marques and Luciane Quoos and Guilherme Tizziotti},
journal= {arXiv preprint arXiv:2605.26263},
year = {2026}
}