论文标题
总和公制的基本属性
Fundamental Properties of Sum-Rank Metric Codes
论文作者
论文摘要
本文研究了单个矩阵块可能具有不同大小的总和度量代码的理论。代码基础性的各种范围以及它们的渐近扩展。还探索了总和度量代码的二重性理论，仅当所有矩阵块都具有相同数量的列时，仅在二重奏代码的二重奏代码（MDS代码的总和类似物）中偶尔。在后一种情况下，二元性考虑因素导致了零件代码块数量的上限。该论文还包含各种构造的总和块大小的总和代码，说明了这些对象在边界，存在和二元性属性方面的可能行为。
This paper investigates the theory of sum-rank metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory of sum-rank metric codes is also explored, showing that MSRD codes (the sum-rank analogue of MDS codes) dualize to MSRD codes only if all matrix blocks have the same number of columns. In the latter case, duality considerations lead to an upper bound on the number of blocks for MSRD codes. The paper also contains various constructions of sum-rank metric codes for variable block sizes, illustrating the possible behaviours of these objects with respect to bounds, existence, and duality properties.
