We consider the notion of a $(q,m)$-polymatroid, due to Shiromoto, and the more general notion of $(q,m)$-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martinez-Penas and Matsumoto for relative generalized rank weights are derived as a consequence.

中文翻译：

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秩度量码广义权重的多拟阵方法

我们考虑 $(q,m)$-polymatroid 的概念，由于 Shiromoto，以及更一般的 $(q,m)$-demi-polymatroid 概念，并展示了如何为它们定义广义权重。此外，我们为这些权重建立了一个对偶性，类似于线性码的广义汉明权重的 Wei 对偶性。因此，推导出了用于 Delsarte 等级度量代码的 Ravagnani 以及相对广义等级权重的 Martinez-Penas 和 Matsumoto 的相应结果。