论文信息 - Translation dual of a semifield

Translation dual of a semifield

In this paper we obtain a new description of the translation dual of a semifield introduced in [G. Lunardon, Translation ovoids, J. Geom. 76 (2003) 200-215]. Using such a description we are able to prove that a semifield and its translation dual have nuclei of the same order. Combining the Knuth cubical array and the translation dual, we give an alternate description of the chain of twelve semifields in the table of [S. Ball, G.L. Ebert, M. Lavrauw, A geometric construction of finite semifields, J. Algebra 311 (2007) 117-129].

[1] P. Dembowski. Finite geometries , 1997 .

[2] Giuseppe Marino,et al. Infinite families of new semifields , 2009, Comb..

[3] Norman L. Johnson,et al. Handbook of Finite Translation Planes , 2007 .

[4] Guglielmo Lunardon. Simplectic spreads and finite semifields , 2007, Des. Codes Cryptogr..

[5] Giuseppe Marino,et al. On Fq-linear sets of PG(3, q3) and semifields , 2007, J. Comb. Theory, Ser. A.

[6] M. Lavrauw. The two sets of three semifields associated with a semifield flock , 2005 .

[7] Joseph A. Thas,et al. Spreads and ovoids in finite generalized quadrangles , 1994 .

[8] Rudolf Lide,et al. Finite fields , 1983 .

[9] Simeon Ball,et al. The six semifield planes associated with a semifield flock , 2004 .

[10] J. Hirschfeld. Finite projective spaces of three dimensions , 1986 .

[11] Giuseppe Marino,et al. Semifields of order q6 with left nucleus Fq3 and center Fq , 2008, Finite Fields Their Appl..

[12] D. Knuth. Finite semifields and projective planes , 1965 .

[13] Michel Lavrauw,et al. A geometric construction of finite semifields , 2007 .