标题： 求和-秩度量码的基本性质 显示英文标题

标题： Fundamental Properties of Sum-Rank Metric Codes

摘要： 本文研究了和-秩度量码的理论，其中各个矩阵块的大小可能不同。 推导了码的基数的各种界，并给出了它们的渐近扩展。 还探讨了和-秩度量码的对偶理论，表明MSRD码（MDS码的和-秩类比）仅当所有矩阵块具有相同列数时，其对偶仍为MSRD码。 在后一种情况下，对偶性考虑导致了MSRD码的块数的一个上界。 本文还包含针对可变块大小的和-秩度量码的各种构造，展示了这些对象在界限、存在性和对偶性质方面的可能行为。 显示英文摘要

摘要： 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.