论文标题
线性切割阻滞集中的新MRD代码
New MRD codes from linear cutting blocking sets
论文作者
论文摘要
最小的等级金属代码或等效地，线性切割阻滞集以第二个广义等级权重来表征，通过与相关$ q $系统的疏忽属性的联系。使用此结果，我们提供了$ \ mathbb {f} _ {q^m} $的第一个构建，该家族的长度为200万美元的线性MRD代码，这些代码未作为两个较小的MRD代码的直接总和。此外，这样的家族具有更好的参数，因为它的代码具有比以前已知的MRD代码的广义等级权重。这表明并非所有MRD代码都具有相同的概括性权重，与锤式度量设置中发生的情况相反。
Minimal rank-metric codes or, equivalently, linear cutting blocking sets are characterized in terms of the second generalized rank weight, via their connection with evasiveness properties of the associated $q$-system. Using this result, we provide the first construction of a family of $\mathbb{F}_{q^m}$-linear MRD codes of length $2m$ that are not obtained as a direct sum of two smaller MRD codes. In addition, such a family has better parameters, since its codes possess generalized rank weights strictly larger than those of the previously known MRD codes. This shows that not all the MRD codes have the same generalized rank weights, in contrast to what happens in the Hamming metric setting.
