Exceptional planar polynomials

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• 作者：Florian Caullery ; Kai-Uwe Schmidt ; Yue Zhou
• 关键词：Planar function ; Exceptional ; Absolutely irreducible polynomial ; Primary ; 11T06 ; Secondary ; 51E20 ; 11T71
• 刊名：Designs, Codes and Cryptography
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：78
• 期：3
• 页码：605-613
• 全文大小：410 KB
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• 作者单位：Florian Caullery (1)
  Kai-Uwe Schmidt (2)
  Yue Zhou (2) (3)
  
  1. Institut de Mathématiques de Luminy, CNRS-UPR9016, 163 av. de Luminy, case 907, 13288, Marseille Cedex 9, France
  2. Faculty of Mathematics, Otto-von-Guericke University, Universitätsplatz 2, 39106, Magdeburg, Germany
  3. Department of Mathematics and System Sciences, College of Science, National University of Defense Technology, Changsha, China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Combinatorics
  Coding and Information Theory
  Data Structures, Cryptology and Information Theory
  Data Encryption
  Discrete Mathematics in Computer Science
  Information, Communication and Circuits
  
• 出版者：Springer Netherlands
• ISSN：1573-7586

文摘

Planar functions are special functions from a finite field to itself that give rise to finite projective planes and other combinatorial objects. We consider polynomials over a finite field \(K\) that induce planar functions on infinitely many extensions of \(K\); we call such polynomials exceptional planar. Exceptional planar monomials have been recently classified. In this paper we establish a partial classification of exceptional planar polynomials. This includes results for the classical planar functions on finite fields of odd characteristic and for the recently proposed planar functions on finite fields of characteristic two. Keywords Planar function Exceptional Absolutely irreducible polynomial