A new construction is given of cyclic semifields of orders q2n, n odd, with kernel (left nucleus) Fq n and right and middle nuclei isomorphic to Fq 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.
On a generalization of cyclic semifields / N. L., Johnson; Marino, Giuseppe; O., Polverino; Trombetti, Rocco. - In: JOURNAL OF ALGEBRAIC COMBINATORICS. - ISSN 0925-9899. - 29:(2009), pp. 1-34. [10.1007/s10801-007-0116-x]
On a generalization of cyclic semifields
MARINO, GIUSEPPE;TROMBETTI, ROCCO
2009
Abstract
A new construction is given of cyclic semifields of orders q2n, n odd, with kernel (left nucleus) Fq n and right and middle nuclei isomorphic to Fq 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.| File | Dimensione | Formato | |
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