Construction of Two Classes of Minimal Binary Linear Codes Based on Boolean Function

被引：0

作者：

Du, Jiawei ^{[1
,2
]}

Du, Xiaoni ^{[1
]}

Jin, Wengang ^{[1
]}

Zhang, Yingzhong ^{[1
]}

机构：

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Gansu, Peoples R China

[2] Guilin Univ Elect Technol, Guangxi Key Lab Cryptog & Informat Secur, Guilin 541004, Guangxi, Peoples R China

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2022年 / E105A卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Boolean function; bent function; Walsh transform; binary linear code; BENT FUNCTIONS;

D O I：

10.1587/transfun.2021EAP1062

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

Linear codes with a few-weight have important applications in combinatorial design, strongly regular graphs and cryptography. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra, and determine their spectrum distribution. Then, we derive two classes of linear codes with at most six-weight from the new functions. Meanwhile, the length, dimension and weight distributions of the codes are obtained. Results show that both of the new codes are minimal and among them, one is wide minimal code and the other is a narrow minimal code and thus can be used to design secret sharing scheme with good access structures. Finally, some Magma programs are used to verify the correctness of our results.

引用

页码：689 / 693

页数：5

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