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两类具有少重量的二元线性码构造.

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Názov: 两类具有少重量的二元线性码构造. (Chinese)
Alternate Title: Construction of Two Classes of Binary Linear Code with a Few Weights. (English)
Autori: 杨志耀, 卓泽朋
Zdroj: Journal of Cryptologic Research (2097-4116); Dec2024, Vol. 11 Issue 6, p1308-1319, 12p
Abstract (English): Linear codes with a few weights have important applications in secret sharing scheme, association scheme, communication systems, etc. In recent years, constructing linear codes from Boolean functions and definition sets is an important research direction in coding field. In this study, by modifying the direct sum construction, some Boolean functions with a few Walsh-spectral are obtained by selecting suitable bent and plateaued functions, and the distribution of its Walsh-spectral are determined. Furthermore, the support set of the Boolean function is selected as the definition set to construct linear codes with a few weights, and their explicit weight distribution are given using the Walsh-spectral. The results show that these codes are all three to six weights, and there are a lot of minimal linear codes. [ABSTRACT FROM AUTHOR]
Abstract (Chinese): 具有少重量的线性码在秘密共享方案、结合方案和通信系统等密码领域发挥着重要作用. 近年 来, 通过选取合适的定义集构造满足要求的线性码是编码领域中重要的研究方向. 修改直和构造并选择合 适的初始 bent 函数和 plateaued 函数, 本文给出了一种具有少谱值的布尔函数的两类构造, 并确定构造 所得布尔函数的 Walsh 谱值分布. 进一步, 选取所得布尔函数的支撑集作为定义集, 构造了具有少重量的 线性码, 并基于 Walsh 谱值分布给出这些码的重量分布. 本文所构造的线性码为三到六重量的、且存在大 量极小线性码． [ABSTRACT FROM AUTHOR]
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Databáza: Complementary Index
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Abstrakt:Linear codes with a few weights have important applications in secret sharing scheme, association scheme, communication systems, etc. In recent years, constructing linear codes from Boolean functions and definition sets is an important research direction in coding field. In this study, by modifying the direct sum construction, some Boolean functions with a few Walsh-spectral are obtained by selecting suitable bent and plateaued functions, and the distribution of its Walsh-spectral are determined. Furthermore, the support set of the Boolean function is selected as the definition set to construct linear codes with a few weights, and their explicit weight distribution are given using the Walsh-spectral. The results show that these codes are all three to six weights, and there are a lot of minimal linear codes. [ABSTRACT FROM AUTHOR]
ISSN:20974116
DOI:10.13868/j.cnki.jcr.000737