Abstract
A new construction is given of cyclic semifields of orders q 2n, n odd, with kernel (left nucleus) \({\mathbb{F}}_{q^{n}}\) and right and middle nuclei isomorphic to \({\mathbb{F}}_{q^{2}}\) , 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 45 and new semifield planes of order 165 are constructed by this method.
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Johnson, N.L., Marino, G., Polverino, O. et al. On a generalization of cyclic semifields. J Algebr Comb 29, 1–34 (2009). https://doi.org/10.1007/s10801-007-0116-x
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DOI: https://doi.org/10.1007/s10801-007-0116-x