On the bijectivity of the map $\chi$

ePrint Report: On the bijectivity of the map $\chi$

Anna-Maurin Graner, Björn Kriepke, Lucas Krompholz, Gohar M. Kyureghyan

We prove that for $n>1$ the map $\chi:\mathbb{F}_q^n \to \mathbb{F}_q^n$, defined by $y=\chi(x)$ with $y_i = x_i + x_{i+2}\cdot(1+x_{i+1})$ for $1\leq i \leq n$, is bijective if and only if
$q=2$ and $n$ is odd, as it was conjectured by Schoone and Daemen in 2023.

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