AI 中文总结
针对MSRD码在部分维度不存在的问题，提出准MSRD（QMSRD）码与对偶QMSRD码，刻画其性质并推导相关分布与广义和秩重量，丰富了和秩度量码的理论体系。
AI 中文摘要
和秩度量码近来因在网络编码、空时码及分布式存储中的应用，受到众多研究者的关注。MSRD码是达到和秩度量下Singleton界的优良码，但在某些维度下不存在。受此事实启发，我们引入准MSRD（QMSRD）码的概念并给出其若干性质。此外，我们发现并非每个QMSRD码都具有QMSRD对偶码，因此定义了对偶QMSRD码，其自身与对偶码均为QMSRD码。最后，我们刻画了这类码，推导了它们的支撑、秩-列表及和秩分布，并计算了它们的广义和秩重量。
英文摘要
Sum-rank-metric codes have recently attracted considerable attention of many researchers, due to their applications in network coding, space-time codes and distributed storage. MSRD codes are those good codes attaining the Singleton bound in the sum-rank metric. However, MSRD codes do not exist for some dimensions. Motivated by this fact, we introduce the notion of quasi-MSRD (QMSRD) codes and provide some properties of them. What is more, we find that not every QMSRD code has a QMSRD dual code, so we give the definition of dually QMSRD codes, whose dual codes and themselves are both QMSRD. Finally, we characterize such codes, derive their support, rank-list and sum-rank distributions as well as compute their generalized sum-rank weights.
Comments24 pages
