定秩集秩度量码的Singleton型上界
Singleton Upper Bound of Rank Metric Codes with Given Ranks
DOI: 10.12677/aam.2026.152075, PDF,    科研立项经费支持
作者: 刘翊文, 陈炫燃, 宋谭夕：苏州科技大学数学科学学院，江苏 苏州；朱博华：石家庄铁道大学数理系，河北 石家庄
关键词: 常维码；定秩集秩度量码；子空间码；Constant Dimension Codes； Rank Metric Codes with Given Ranks； Subspace Codes
摘要: 为了推动网络编码实用化，2006年Médard等人提出随机网络编码概念，2008年Kschischang等人针对错误纠正与数据恢复需求，提出子空间码模型，而定秩集秩度量码是用来构造子空间码的一类辅助码。我们的研究围绕网络编码范畴展开，主要针对常维码与定秩集秩度量码这两类核心研究对象。在网络编码基本原理的基础上，本文系统地研究了定秩集秩度量码的代数性质，给出了定秩集秩度量码的Singleton界，证明了定秩集秩度量码的渐近最优性。
Abstract: To promote the practical application of network coding, Médard et al. proposed the concept of random network coding in 2006. In 2008, to address the requirements of error correction and data recovery, Kschischang et al. put forward the subspace code model, where rank metric codes with given ranks serve as a class of auxiliary codes for constructing subspace codes. Our research focuses on the field of network coding, with its primary focus on two core research objects: constant dimension codes and rank metric codes with given ranks. Based on the fundamental principles of network coding, this paper systematically investigates the algebraic properties of rank metric codes with given ranks, derives the Singleton upper bound for such codes, and proves their asymptotic optimality.
文章引用：刘翊文, 陈炫燃, 宋谭夕, 朱博华. 定秩集秩度量码的Singleton型上界[J]. 应用数学进展, 2026, 15(2): 345-351. https://doi.org/10.12677/aam.2026.152075

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