Planar Functions and Planes of Lenz-Barlotti Class II

被引：222
作者：
Coulter R.S. [1 ]
Matthews R.W. [1 ]
机构：
[1] Department of Computer Science, University of Queensland, St. Lucia
来源：
Designs, Codes and Cryptography | 1997年 / 10卷 / 2期
关键词：
Finite fields; Permutation polynomials; Planar functions; Projective planes;
D O I：
10.1023/A:1008292303803
中图分类号：
学科分类号：
摘要：
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 y 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.
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收藏
页码：167 / 184
页数：17
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