[1]黄冬梅,唐春明.一类二次Bent函数的有效构造[J].西华师范大学学报(自然科学版),2017,38(01):80-86.[doi:10.16246/j.issn.1673-5072.2017.01.014]
 HUANG Dongmei,TANG Chunming.Effective Construction of a Class of Bent Quadratic Boolean Functions[J].Journal of China West Normal University(Natural Sciences),2017,38(01):80-86.[doi:10.16246/j.issn.1673-5072.2017.01.014]
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一类二次Bent函数的有效构造()
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《西华师范大学学报(自然科学版)》[ISSN:1673-5072/CN:51-1699/N]

卷:
38
期数:
2017年01期
页码:
80-86
栏目:
出版日期:
2017-03-20

文章信息/Info

Title:
Effective Construction of a Class of Bent Quadratic Boolean Functions
作者:
黄冬梅唐春明
( 西华师范大学 数学与信息学院,四川 南充637009)
Author(s):
HUANG DongmeiTANG Chunming
(College of Mathematic and Information,China West Normal University,Nanchong Sichuan 637009,China)
关键词:
Bent函数布尔函数Walsh-Hadamard变换分圆多项式半Bent函数
Keywords:
Bent functionsBoolean functionsWalshHadamard transformcyclotomic polynomialssemibent functions
分类号:
TN918.1
DOI:
10.16246/j.issn.1673-5072.2017.01.014
文献标志码:
A
摘要:
Bent函数在图论、组合设计、密码学和通信理论中都有着重要的应用, 可以用来构造强正则图、对称密码中的S盒、序列、结合方案和编码等。 Bent函数的完全刻画是非常困难的问题, 许多研究工作主要围绕特殊形式Bent函数的刻画和构造。考虑一类二次Bent函数性质的刻画和构造, 利用分圆多项式的性质, 使用二次Bent函数对应多项式的系数, 详细刻画了两种情形下的二次Bent函数的Bent性, 并在第二种情形下, 对二次Bent函数计数。
Abstract:
Bent functions have many applications of great importance in graph theory,combinatorial design theory,cryptography and communications for the constructing of strong regular graphs,Sboxes in symmetric cryptography,sequences,association schemes,codes and so on.It is of great difficulty to completely characterize bent functions.Therefore,lots of research work mainly focuses on the characterization and construction of special bent functions.This paper talks about the characterization and construction of a class of quadratic bent functions by using properties of cyclotomic polynomials and their polynomial coefficients to present detailed characterization of quadratic bent functions in two cases and enumerates the number of quadratic bent functions in the second case.

参考文献/References:


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备注/Memo

备注/Memo:

收稿日期:2016-06-10基金项目:国家自然科学基金项目(11401480)
作者简介:黄冬梅(1980—),女,湖北荆州人,讲师,主要从事组合优化和编码研究。
通信作者:黄冬梅,E-mail: dongmeih_math@163.com
引用本文:黄冬梅,唐春明.一类二次Bent函数的有效构造[J].西华师范大学学报(自然科学版),2017,38(1):80-86.[HUANG Dongmei,TANG Chunming.Effective construction of a class of Bent quadratic Boolean functions[J].Journal of China West Normal University(Natural Sciences),2017,38(1):80-86.]一类二次Bent函数的有效构造
更新日期/Last Update: 2017-03-20