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A note on commutative semifield planes

  • Yue Zhou EMAIL logo
Published/Copyright: June 9, 2017
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Advances in Geometry
From the journal Advances in Geometry Volume 18 Issue 1

Abstract

Let q be an odd prime power. We prove that a planar function f from 𝔽q to itself can be written as an affine Dembowski–Ostrom polynomial if and only if the projective plane derived from f is a commutative semifield plane.

Keywords: Planar function; relative difference set; semifield plane
MSC 2010: 12K10; 51A35; 12E10

Communicated by: G. Korchmáros

  1. Funding: Yue Zhou is partially supported by the National Natural Science Foundation of China (No. 11401579, 11531002) and the Research Project of MIUR (Italian Office for University and Research) “Strutture geometriche, Combinatoria e loro Applicazioni” 2012.

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Received: 2015-9-30
Revised: 2016-4-30
Published Online: 2017-6-9
Published in Print: 2018-1-26

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  3. The non-solvable doubly transitive dimensional dual hyperovals
  5. On the real differential of a slice regular function
  7. Generalized null 2-type immersions in Euclidean space
  9. A dual rigidity of the sphere and the hyperbolic plane
  11. The conjugacy locus of Cayley–Salmon lines
  13. Steiner’s Porism in finite Miquelian Möbius planes
  15. Enumeration of complex and real surfaces via tropical geometry
  17. On complete Yamabe solitons
  19. Polytopal approximation of elongated convex bodies
  21. A note on commutative semifield planes
  23. Quartic surfaces with icosahedral symmetry
https://doi.org/10.1515/advgeom-2017-0017
Keywords for this article
Planar function; relative difference set; semifield plane

Articles in the same Issue

  1. Frontmatter
  3. The non-solvable doubly transitive dimensional dual hyperovals
  5. On the real differential of a slice regular function
  7. Generalized null 2-type immersions in Euclidean space
  9. A dual rigidity of the sphere and the hyperbolic plane
  11. The conjugacy locus of Cayley–Salmon lines
  13. Steiner’s Porism in finite Miquelian Möbius planes
  15. Enumeration of complex and real surfaces via tropical geometry
  17. On complete Yamabe solitons
  19. Polytopal approximation of elongated convex bodies
  21. A note on commutative semifield planes
  23. Quartic surfaces with icosahedral symmetry
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