More on quadratic functions and maximal Artin–Schreier curves

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• 作者：Nurdagül Anbar ; Wilfried Meidl
• 关键词：Artin–Schreier curve ; Partially bent function ; Quadratic function ; Walsh transform ; 11G20 ; 11E04 ; 11T23 ; 11T71
• 刊名：Applicable Algebra in Engineering, Communication and Computing
• 出版年：2015
• 出版时间：November 2015
• 年：2015
• 卷：26
• 期：5
• 页码：409-426
• 全文大小：477 KB
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• 作者单位：Nurdagül Anbar (1)
  Wilfried Meidl (2)
  
  1. Max Planck Institute for Mathematics, 53111, Bonn, Germany
  2. Sabanc? University, MDBF, Orhanl?, Tuzla, 34956, Istanbul, Turkey
  
• 刊物类别：Computer Science
• 刊物主题：Symbolic and Algebraic Manipulation
  Computer Hardware
  Theory of Computation
  Artificial Intelligence and Robotics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0622

文摘

For an odd prime \(p\) and an even integer \(n\) with \(\gcd (n,p) > 1\), we consider quadratic functions from \({\mathbb F}_{p^{n}}\) to \({\mathbb F}_p\) of codimension \(k\). For various values of \(k\), we obtain classes of quadratic functions giving rise to maximal and minimal Artin–Schreier curves over \({\mathbb F}_{p^{n}}\). We completely classify all maximal and minimal curves obtained from quadratic functions of codimension \(2\) and coefficients in the prime field \({\mathbb F}_p\). The results complement our results obtained earlier for the case \(\gcd (n,p) = 1\). The arguments are more involved than for the case \(\gcd (n,p) = 1\). Keywords Artin–Schreier curve Partially bent function Quadratic function Walsh transform