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Solution to An Isotopism Question Concerning Rank 2 Semifields
Author(s) -
Lavrauw Michel,
Marino Giuseppe,
Polverino Olga,
Trombetti Rocco
Publication year - 2015
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21382
Subject(s) - rank (graph theory) , mathematics , combinatorics , order (exchange) , algebra over a field , pure mathematics , finance , economics
In [8] Dempwolff gives a construction of three classes of rank two semifields of order q 2 n , 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 .