A geometric construction of finite semifields

DOI10.1016/j.jalgebra.2006.11.044zbMath1125.12002OpenAlexW1970310746MaRDI QIDQ877699

Simeon Ball, Michel Lavrauw, Gary L. Ebert

Publication date: 3 May 2007

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.11.044

zbMATH Keywords

spreadssemifieldsaffine planestranslation planes

Mathematics Subject Classification ID

Finite affine and projective planes (geometric aspects) (51E15) Semifields (12K10)

Related Items (22)

\(S_3\) invariants of finite dimensional real division algebras ⋮ 50 years of translation structures ⋮ Finite semifields: A brief history and current directions ⋮ A new family of linear maximum rank distance codes ⋮ ON THE PRODUCT OF ELEMENTS WITH PRESCRIBED TRACE ⋮ The BEL-rank of finite semifields ⋮ Some recent directions in finite semifields ⋮ The generalized translation dual of a semifield ⋮ Projective planes of Lenz-Barlotti class V. ⋮ Segre embeddings and finite semifields ⋮ Finite semifields and nonsingular tensors ⋮ Linearized polynomials and their adjoints, and some connections to linear sets and semifields ⋮ The 2‐Blocking Number and the Upper Chromatic Number of PG(2,q) ⋮ On the isotopism classes of finite semifields ⋮ Translation dual of a semifield ⋮ Solution to An Isotopism Question Concerning Rank 2 Semifields ⋮ Linear sets in finite projective spaces ⋮ On the intersection problem for linear sets in the projective line ⋮ HMO-planes ⋮ On a generalization of cyclic semifields ⋮ Finite semifields with a large nucleus and higher secant varieties to Segre varieties ⋮ On BEL-configurations and finite semifields

Uses Software

• Magma

Cites Work

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• Planar functions and planes of Lenz-Barlotti class II
• Finite Sperner spaces constructed from projective and affine spaces
• Translation planes of order 27
• On the classification of semifield flocks.
• Commutative semifields and symplectic spreads.
• The six semifield planes associated with a semifield flock
• Finite semifields and projective planes
• Sublines of prime order contained in the set of internal points of a conic
• Semifield planes of order \(q^4\) with kernel \(\mathbb F_{q^2}\) and center \(\mathbb F_q\)
• The two sets of three semifields associated with a semifield flock
• Generalized twisted fields
• Symplectic semifield planes and ℤ₄–linear codes

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