On semifields of type (q2n,qn,q2,q2,q), n odd
Giuseppe Marino, Olga Polverino, Rocco Trombetti · Innovations in incidence geometry · 2008
A semifield of type (q 2n , q n , q 2 , q 2 , q) (with n > 1) is a finite semifield of order q 2n (q a prime power) with left nucleus of order q n , right and middle nuclei both of order q 2 and center of order q.Semifields of type (q 6 , q 3 , q 2 , q 2 , q) have been completely classified by the authors and N. L. Johnson in [10].In this paper we determine, up to isotopy, the form of any semifield of type (q 2n , q n , q 2 , q 2 , q) when n is an odd integer, proving that there exist n-1 2 non isotopic potential families of semifields of this type.Also, we provide, with the aid of the computer, new examples of semifields of type (q 14 , q 7 , q 2 , q 2 , q), when q = 2.