Planar Functions and Planes of Lenz-Barlotti Class II
- 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  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 . 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.