常维码的多重构造方法的新改进
New Improvements of Multilevel Construction for Constant Dimension Codes
DOI: 10.12677/AAM.2023.124198, PDF,    科研立项经费支持
作者: 李 可*, 吴温萱, 郭芝燕, 杜雨轩：苏州科技大学数学科学学院，江苏 苏州
关键词: 秩度量码；多重构造；常维码；Rank-Metric Code； Multilevel Construction； Constant Dimension Code
摘要: 常维码(constant dimension codes)作为一种特殊的子空间码，由于其在随机网络编码中的应用而受到关注。Etzion等人在[IEEE Trans. Inf. Theory, 55 (2009), 2909–2919.]给出了子空间距离与汉明距离、秩距离之间的关系，并提出了构造常维码的一种重要方法——多重构造法，此构造法也已被众多学者进行了推广。本文在原多重构造的基础上，利用待定点增加子空间距离的思想更加精细地刻画了子空间距离与汉明距离之间的关系，由此给出了寻找子空间码标识向量更一般的方法，利用此方法提升了(14,6,4)q-常维码的下界。
Abstract: Constant dimension codes (CDCs), as special subspace codes, have received a lot of attention due to its application in random network coding. Multilevel construction, as an important construction of CDCs, was raised by Etzion et al. in [IEEE Trans. Inf. Theory, 55 (2009), 2909–2919.] by explaining the relation between subspace distance and Hamming distance, rank distance. This construction has also been generalized by many scholars. Based on the original multilevel construction, the pa-per uses the idea of increasing subspace distance by fixing pending dots to more delicately describe the relationship between subspace distance and Hamming distance. Therefore, we provide a more general method for finding the identifying vectors of subspace codes and also improve the lower bound of (14,6,4)q -CDC.
文章引用：李可, 吴温萱, 郭芝燕, 杜雨轩. 常维码的多重构造方法的新改进[J]. 应用数学进展, 2023, 12(4): 1927-1939. https://doi.org/10.12677/AAM.2023.124198

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