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对于m-Spotty重量计数器在ZpRk上的麦克威廉姆斯身份
Juan Wang1, An Jiang2, Patrick Solé3
1Department of Base Courses, Anhui Sanlian University, Hefei 230601, China.
Entropy (Basel, Switzerland)
|January 28, 2026
概括
这项研究探讨了在混合字母ZpRk上的m点重量计数器,并使用新的灰色地图和概括的哈达马德变换建立了线性代码及其二元的麦克威廉姆斯身份.
科学领域:
- 编码理论编码理论
- 抽象代数 抽象代数
- 离散的数学 离散的数学
背景情况:
- 在编码理论中,对重量计数器的研究对于理解代码属性至关重要.
- 像ZpRk这样的混合字母表在代数分析中提出了独特的挑战.
- 之前的工作集中在更简单的字母表上,需要扩展混合结构.
研究的目的:
- 在混合字母ZpRk.k.上研究m点的重量计数器.
- 为了在ZpRk设置中确定这些计数器的MacWilliams标识.
- 引入一种通用框架,用于分析混合字母的代码.
主要方法:
- 从Zpα×Rkβ到Zpα+kβ的灰色地图的构建.
- 应用了一般化的哈达马德变换.
- 运用Zp的正规添加性特征进行代数分析.
主要成果:
- 成功构建了Gray地图,用于指定的混合字母.
- 在ZpRk.上建立了m-spotty重量计数器的MacWilliams标识.
- 提供了适用于线性代码及其对ZpRk的双重函数的理论框架.
结论:
- 通过一个示例来验证理论结果.
- 这些发现将麦克威廉姆斯身份的适用性扩展到更复杂的代码结构.
- 这项工作为分析混合字母的代码提供了新的工具.
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