JOURNAL OF
ALGEBRAIC
COMBINATORICS

Home > Vol 29, No 1 (2009)

Norman L. Johnson¹ , Giuseppe Marino² , Olga Polverino³ and Rocco Trombetti²

¹University of Iowa Mathematics Dept. Iowa City IA 52242 USA
²Università degli Studi di Napoli “Federico II” Dipartimento di Matematica e Applicazioni 80126 Napoli Italy
³Seconda Università degli Studi di Napoli Dipartimento di Matematica 81100 Caserta Italy

A new construction is given of cyclic semifields of orders q ^{2 n} , n odd, with kernel (left nucleus) \mathbb F _{q ⁿ} {\mathbb{F}}_{q^{n}} and right and middle nuclei isomorphic to \mathbb F _{q ²} {\mathbb{F}}_{q^{2}} , and the isotopism classes are determined. Furthermore, this construction is generalized to produce potentially new semifields of the same general type that are not isotopic to cyclic semifields. In particular, a new semifield plane of order 4 ⁵ and new semifield planes of order 16 ⁵ are constructed by this method.

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