On a generalization of cyclic semifields
The authors give a new construction of cyclic semifields of order \(q^{2n}\), \(n\) odd, left nucleus \(\mathbb{F}_{q^n}\) and right and middle nucleus isomorphic to \(\mathbb{F}_{q^2}\). They determine the isotopism classes. This construction is then generalized to produce potentially new semifields that are not isotopic to cyclic semifields. In this way, new semifields of order \(4^5\) and \(16^5\) are obtained. The authors also show that these semifields are new.
scientific article; zbMATH DE number 5550556