基于线性切割块集的新MRD码
New MRD codes from linear cutting blocking sets
摘要：
最小秩度量码或等价的线性截块集的特征在于第二广义秩权重，通过它们与相关的$q$ -系统的回避性质的连接。使用这个结果，我们提供了第一个家庭的$\mathbb{F}_{q^m}$ -线性MRD码的长度$2m$，而不是作为一个直和的两个较小的MRD码。此外，这样的家庭有更好的参数，因为它的代码具有广义秩权重严格大于那些以前已知的MRD码。这表明并非所有的MRD码都具有相同的广义秩权重，与汉明度量设置中发生的情况相反。
英文摘要：
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.
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