Bent Vectorial Functions, Codes and Designs

Ding Cunsheng; Munemasa Akihiro; Tonchev Vladimir D.

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Bent Vectorial Functions, Codes and Designs

机译：弯曲的矢量功能，代码和设计

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Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group (GF(2(2m)),+), have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold 2-designs. A new coding-theoretic characterization of bent vectorial functions is presented.

机译：Bent函数或等效的是基本Abelian组（GF（2（2m）），+）中的Hadamard差集已用于构造具有对称差属性的对称和准对称设计。本文的主要目的是使用弯曲矢量函数构造二参数线性二进制代码族，这些二元线性代码不满足Assmus-Mattson定理的条件，但仍具有2-设计。提出了弯曲矢量函数的一种新的编码理论表征。

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来源
《IEEE Transactions on Information Theory》 |2019年第11期|7533-7541|共9页
作者
Ding Cunsheng; Munemasa Akihiro; Tonchev Vladimir D.;
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作者单位

Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Peoples R China;

Tohoku Univ Grad Sch Informat Sci Res Ctr Pure & Appl Math Sendai Miyagi 9808579 Japan;

Michigan Technol Univ Dept Math Sci Houghton MI 49931 USA;

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正文语种 eng
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关键词
Bent function; bent vectorial function; linear code; 2-design;

机译：弯曲功能弯曲矢量功能线性代码2设计;

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1. Bent vectorial functions and linear codes from o-polynomials [J] . Mesnager Sihem Designs, Codes and Crytography . 2015,第1期

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2. BENT AND VECTORIAL BENT FUNCTIONS, PARTIAL DIFFERENCE SETS, AND STRONGLY REGULAR GRAPHS [J] . Cesmelioglu Ayca, Meidl Wilfried Advances in mathematics of communications . 2018,第4期

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3. On Design-Theoretic Aspects of Boolean and Vectorial Bent Function [J] . Alexandr A. Polujan, Alexander Pott IEEE Transactions on Information Theory . 2021,第2期

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4. On vectorial bent functions with Dillon-type exponents [C] . Lucien Lapierre, Petr Lisoněk IEEE International Symposium on Information Theory . 2016

机译：Dillon型指数的向量弯曲函数
5. Digital image coding techniques: Codec design using vector quantization method. [D] . Shin, Yong Ho. 1994

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6. Advanced Design of Dumbbell-shaped Genetic Minimal Vectors Improves Non-coding and Coding RNA Expression [O] . Xiaoou Jiang, Han Yu, Cui Rong Teo, 2016

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7. Bent and vectorial bent functions, partial difference sets, and strongly regular graphs [O] . Ayça Çeşmelioğlu, Wilfried Meidl 2018

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Bent Vectorial Functions, Codes and Designs

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