In [8] Dempwolff gives a construction of three classes of rank two semifields of order $q^2n$, with $q$ and $n$ odd, using Dembowski–Ostrom polynomials. The question whether these semifields are new, i.e. not isotopic to previous constructions, is left as an open problem. In this paper we solve this problem for $n > 3$, in particular we prove that two of these classes, labeled D A and D A B, are new for $n > 3$, whereas presemifields in family D B are isotopic to Generalized Twisted Fields for each $n ≥ 3$.

Solution to an isotopism question conerning rank 2 semifields / Lavrauw, M.; Marino, G.; Polverino, O.; Trombetti, Rocco. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 23:2(2015), pp. 60-77. [10.1002/jcd.21382]

Solution to an isotopism question conerning rank 2 semifields

G. Marino;TROMBETTI, ROCCO
2015

Abstract

In [8] Dempwolff gives a construction of three classes of rank two semifields of order $q^2n$, with $q$ and $n$ odd, using Dembowski–Ostrom polynomials. The question whether these semifields are new, i.e. not isotopic to previous constructions, is left as an open problem. In this paper we solve this problem for $n > 3$, in particular we prove that two of these classes, labeled D A and D A B, are new for $n > 3$, whereas presemifields in family D B are isotopic to Generalized Twisted Fields for each $n ≥ 3$.
2015
Solution to an isotopism question conerning rank 2 semifields / Lavrauw, M.; Marino, G.; Polverino, O.; Trombetti, Rocco. - In: JOURNAL OF COMBINATORIAL DESIGNS. - ISSN 1063-8539. - 23:2(2015), pp. 60-77. [10.1002/jcd.21382]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11588/573089
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