A generalization of some Huang-Johnson semifields

作者：Johnson N L^*; Marino Giuseppe; Polverino Olga; Trombetti Rocco

来源：Electronic Journal of Combinatorics, 2011, 18(1): 29.

In [H. Huang, N.L. Johnson: Semifield planes of order 8(2), Discrete Math., 80 (1990)], the authors exhibited seven sporadic semifields of order 26, with left nucleus F-2(3) and center F-2. Following the notation of that paper, these examples are referred as the Huang-Johnson semifields of type II, III, IV, V, VI, VII and VIII. In [N. L. Johnson, V. Jha, M. Biliotti: Handbook of Finite Translation Planes, Pure and Applied Mathematics, Taylor Books, 2007], the question whether these semifields are contained in larger families, rather then sporadic, is posed. In this paper, we first prove that the Huang-Johnson semifield of type VI is isotopic to a cyclic semifield, whereas those of types VII and VIII belong to infinite families recently constructed in [N.L. Johnson, G. Marino, O. Polverino, R. Trombetti: Semifields of order q(6) with left nucleus F-q(3) and center Fq (,)Finite Fields Appl., 14 (2008)] and [G.L .Ebert,G.Marino, O. Polverino, R.Trombetti: Infinite families of new semifields, Combinatorica, 6 (2009)]. Then, Huang-Johnson semifields of type II and III are extended to new infinite families of semifields of order q(6), existing for every prime power q.

• 出版日期2011-2-4