On some classes of codes with a few weights

Yiwei Liu; Zihui Liu

doi:10.3934/amc.2018025

On some classes of codes with a few weights

Yiwei Liu
, Zihui Liu^*

^*此作品的通讯作者

数学学院

Beijing Institute of Technology

科研成果: 期刊稿件 › 文章 › 同行评审

10 引用（Scopus）

摘要

We generalize the code constructed recently by Wang et al, and obtain many classes of codes with a few weights. The weight distribution of these codes is completely determined, and the minimum distance of the duals of these codes is determined. We also show that some subclasses of the duals of these codes are optimal. Furthermore, some parameters of the generalized Hamming weight of these codes are calculated in certain cases.

源语言	英语
页（从-至）	415-428
页数	14
期刊	Advances in Mathematics of Communications
卷	12
期	2
DOI	https://doi.org/10.3934/amc.2018025
出版状态	已出版 - 2018

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10.3934/amc.2018025

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title = "On some classes of codes with a few weights",

abstract = "We generalize the code constructed recently by Wang et al, and obtain many classes of codes with a few weights. The weight distribution of these codes is completely determined, and the minimum distance of the duals of these codes is determined. We also show that some subclasses of the duals of these codes are optimal. Furthermore, some parameters of the generalized Hamming weight of these codes are calculated in certain cases.",

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AB - We generalize the code constructed recently by Wang et al, and obtain many classes of codes with a few weights. The weight distribution of these codes is completely determined, and the minimum distance of the duals of these codes is determined. We also show that some subclasses of the duals of these codes are optimal. Furthermore, some parameters of the generalized Hamming weight of these codes are calculated in certain cases.

KW - Generalized Hamming weight

KW - Primitive root

KW - Secret sharing scheme

KW - Trace function

KW - Weight distribution

UR - https://www.scopus.com/pages/publications/85046448058

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DO - 10.3934/amc.2018025

M3 - Article

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VL - 12

SP - 415

EP - 428

JO - Advances in Mathematics of Communications

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On some classes of codes with a few weights

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