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New pseudo-planar binomials in characteristic two and related schemes

机译：特征二及其相关方案中的新伪平面二项式

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摘要

Planar functions in odd characteristic were introduced by Dembowski and Ostrom in order to construct finite projective planes in 1968. They were also used in the constructions of DES-like iterated ciphers, error-correcting codes, and signal sets. Recently, a new notion of pseudo-planar functions in even characteristic was proposed by Zhou. These new pseudo-planar functions, as an analogue of planar functions in odd characteristic, also bring about finite projective planes. There are three known infinite families of pseudo-planar monomial functions constructed by Schmidt and Zhou, and Scherr and Zieve. In this paper, three new classes of pseudo-planar binomials are provided. Moreover, we find that each pseudo-planar function gives an association scheme which is defined on a Galois ring.
机译：Dembowski和Ostrom在1968年引入了具有奇特征的平面函数，以构造有限的射影平面。它们还用于构造类似DES的迭代密码，纠错码和信号集。最近，Zhou提出了偶数特征的伪平面函数的新概念。这些新的伪平面函数作为具有奇特征的平面函数的类似物，也带来了有限的投影平面。 Schmidt和Zhou以及Scherr和Zieve构造了三个已知的伪平面单项式函数无限族。本文提供了三类新的伪平面二项式。此外，我们发现每个伪平面函数都给出了在Galois环上定义的关联方案。

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  • 来源
    《Designs, Codes and Crytography》 |2015年第2期|345-360|共16页
  • 作者

    Hu Sihuang; Li Shuxing; Zhang Tao; Feng Tao; Ge Gennian;

  • 作者单位

    Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China;

    Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China;

    Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China;

    Zhejiang Univ, Dept Math, Hangzhou 310027, Zhejiang, Peoples R China|Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing 100048, Peoples R China;

    Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China|Beijing Ctr Math & Informat Interdisciplinary Sci, Beijing 100048, Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Pseudo-planar function; Relative difference set; Projective plane; Association scheme;

    机译：伪平面函数相对差集投影平面关联方案;

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