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math.CO2026
Commutative Semifields from bijections of the Desarguesian plane
Faruk Göloğlu, Lukas Kölsch
The Menichetti-Kaplansky theorem states that a finite semifield that is three-dimensional over its center is either a field or a twisted field of Albert. This implies that a quadra…
math.CO2023★ 8 cited
Value Distributions of Perfect Nonlinear Functions
Lukas Kölsch, Alexandr Polujan
In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we deve…
math.CO2020★ 2 cited
Image sets of perfectly nonlinear maps
Lukas Kölsch, Björn Kriepke, Gohar M. Kyureghyan
We consider image sets of differentially -uniform maps of finite fields. We present a lower bound on the image size of such maps and study their preimage distribution, by extend…