Commutative Semifields of Rank 2 Over Their Middle Nucleus

Simeon Ball and Michel Lavrauw
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Simeon Ball: University of London, Queen Mary
Michel Lavrauw: Eindhoven University of Technology

A chapter in Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, 2002, pp 1-21 from Springer

Abstract: Abstract This article is about finite commutative semifields that are of rank 2 over their middle nucleus, the largest subset of elements that is a finite field. These semifields have a direct correspondence to certain flocks of the quadratic cone in PG(3, q) and to certain ovoids of the parabolic space Q(4, q). We shall consider these links, the known examples and non-existence results.

Keywords: Projective Plane; Finite Field; Internal Point; Generalize Quadrangle; Translation Plane (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-59435-9_1

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DOI: 10.1007/978-3-642-59435-9_1

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