Translation dual of a semifield
A new description of the translation dual of a semifield introduced by \textit{G. Lunardon} [J. Geom. 76, No. 1--2, 200--215 (2003; Zbl 1042.51008)] is presented. Using this description, it is proved that a semifield and its translation dual have nuclei of the same order. Combining the Knuth cubical array and the translation dual, an alternate description of the chain of twelve semifields in the table obtained by \textit{S. Ball, G. L. Ebert} and \textit{M. Lavrauw} [J. Algebra 311, No. 1, 117--129 (2007; Zbl 1125.12002)] is also presented.
scientific article; zbMATH DE number 5379260
scientific article