An in-depth study of the power function $x^{q+2}$ over the finite field ${\mathbb{F}}_{q^2}$: the differential, boomerang, and Walsh spectra, with an application to coding theory

Sihem Mesnager, Huawei Wu

Let $q=p^m$, where $p$ is an odd prime number and $m$ is a positive integer. In this paper, we examine the finite field ${\mathbb{F}}_{q^2}$, which consists of $q^2$ elements. We f…