MacWilliams duality and a Gleason-type theorem on self-dual bent functions

ong Yoon Hyun; Heisook Lee; Yoonjin Lee

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MacWilliams duality and a Gleason-type theorem on self-dual bent functions

机译：MacWilliams对偶性和自对偶弯曲函数的Gleason型定理

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摘要

We prove that the MacWilliams duality holds for bent functions. It enables us to derive the concept of formally self-dual Boolean functions with respect to their near weight enumerators. By using this concept, we prove the Gleason-type theorem on self-dual bent functions. As an application, we provide the total number of (self-dual) bent functions in two and four variables obtaining from formally self-dual Boolean functions.

机译：我们证明MacWilliams对偶性对于弯曲函数成立。它使我们能够针对它们的近似权重枚举数派生形式上自对偶布尔函数的概念。通过使用这个概念，我们证明了关于自对偶弯曲函数的格里森型定理。作为应用程序，我们提供了从形式上自对偶布尔函数获得的两个和四个变量中（自对偶）弯曲函数的总数。

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来源
《Designs, Codes and Crytography》 |2012年第3期|p.295-304|共10页
作者
ong Yoon Hyun; Heisook Lee; Yoonjin Lee;
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作者单位

Institute of Mathematical Sciences, Ewha Womans University, Seoul 120-750, South Korea;

Department of Mathematics, Ewha Womans University, Seoul 120-750, South Korea;

Department of Mathematics, Ewha Womans University, Seoul 120-750, South Korea;

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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
self-dual bent function; formally self-dual boolean function; gleason theorem; MacWilliams duality;

机译：自双弯曲功能;正式的自我对偶布尔函数;格里森定理MacWilliams对偶;

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1. ON THE DUAL OF (NON)-WEAKLY REGULAR BENT FUNCTIONS AND SELF-DUAL BENT FUNCTIONS [J] . Ay?a ?e?melio?lu, Wilfried Meidl, Alexander Pott Advances in mathematics of communications . 2013,第4期

机译：关于（非）弱正规弯曲函数和自对双弯曲函数的对偶
2. Metrical properties of self-dual bent functions [J] . Kutsenko Aleksandr Designs, Codes and Crytography . 2020,第1期

机译：自对折函数的度量性质
3. The group of automorphisms of the set of self-dual bent functions [J] . Kutsenko Aleksandr Cryptography and Communications . 2020,第5期

机译：这组自双弯曲功能集的自动态
4. Duality Theorems of Multiobjective Programming for a Class of Generalized Convex Functions [C] . Wang Jing, Zhen Kaiwei International Conference on Management Science Engineering . 2007

机译：一类广义凸函数的多目标规划对偶性定理
5. Index theorems for anti-self-dual and self-dual orbifolds [D] . Lock, Michael T. 2013

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6. Solutions to Yang—Mills equations that are not self-dual [O] . L. M. Sibner, R. J. Sibner, K. Uhlenbeck 1989

机译：非对偶的杨-米尔斯方程的解
7. On the dual of (non)-weakly regular bent functions and self-dual bent functions [O] . Ceşmelioğlu Ayça, Cesmelioglu Ayca, Meidl Wilfried, 2013

机译：关于（非）弱正则弯曲函数和自对偶弯曲函数的对偶

MacWilliams duality and a Gleason-type theorem on self-dual bent functions

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