The Characteristic of Quadratic Bent Functions and Its Applications

ZHANG Wen-ying; LI Shi-qu

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The Characteristic of Quadratic Bent Functions and Its Applications

更新时间：2025-07-16

- The Characteristic of Quadratic Bent Functions and Its Applications
- Acta Electronica Sinica Vol. 32, Issue 4, Pages: 654-656(2004)
- 作者机构：
  
  郑州信息工程学院信息研究系,河南,郑州,450002
- 作者简介：
- 基金信息：
- DOI：
  CLC： TN918.1
- Published：2004
- 稿件说明：
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ZHANG Wen-ying, LI Shi-qu. The Characteristic of Quadratic Bent Functions and Its Applications[J]. Acta Electronica Sinica, 2004, 32(4): 654-656.
DOI：

ZHANG Wen-ying, LI Shi-qu. The Characteristic of Quadratic Bent Functions and Its Applications[J]. Acta Electronica Sinica, 2004, 32(4): 654-656. DOI：

摘要

本文证明了任意代数次数为2的

元Bent函数都与形式为

+…+x

n-1

的Bent函数线性等价;给出了以任意已知代数次数为2的

元Bent函数为分量的多维Bent函数的构造法;利用本文所给的方法

对任一主对角线上元素全为0的

阶可逆对称矩阵

都可以构造k

-1个主对角线上元素全为0的

n阶可逆对称矩阵M

…

使得M

…

的任意非零线性组合仍是主对角线上元素全为0的阶可逆对称矩阵.

Abstract

This paper gives a proof that all Bent functions of degree 2 are linearly equivalent each other and presents a method for constructing

multi—dimension Bent

functions when one output variable is of degree 2.For a given reversible symmetrical matrix with the elements of its diagonal is 0

it provides a method for constructing

-1's reversible symmetrical matrixes

such that every non-zero linear combination of these

's matrixes is also a reversible symmetrical matrix.

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