Designs, Codes and Cryptography

, Volume 10, Issue 2, pp 167–184

Planar Functions and Planes of Lenz-Barlotti Class II

  • Robert S. Coulter
  • Rex W. Matthews

DOI: 10.1023/A:1008292303803

Cite this article as:
Coulter, R.S. & Matthews, R.W. Designs, Codes and Cryptography (1997) 10: 167. doi:10.1023/A:1008292303803


Planar functions were introduced by Dembowski and Ostrom [4] to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a question posed in [4]. These planar functions define at least one such affine plane of order 3e for every e ≥ 4 and their projective closures are of Lenz-Barlotti type II. All previously known planes of type II are obtained by derivation or lifting. At least when e is odd, the planes described here cannot be obtained in this manner.

planar functions projective planes permutation polynomials finite fields 

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Robert S. Coulter
  • Rex W. Matthews

There are no affiliations available