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Commutative Semifields from bijections of the Desarguesian plane
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 quadratic homogeneous bijection of $\mathbb{P}^2(\mathbb{F}_q)$ is equivalent to a Dembowski-Ostrom monomial. In this paper, w
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