论文标题
回避子空间，广义排名权重和接近MRD代码
Evasive subspaces, generalized rank weights and near MRD codes
论文作者
论文摘要
我们对$ \ Mathbb {f} _ {q^m} $ - 线性级别级代码和避相关$ \ mathbb {f} _q $ -subspaces的$ \ mathbb {f} _} _ {q^m}^k $之间的连接之间的连接。我们给出了一个统一的框架，在该框架中，我们以基本的方式证明了等级代码的参数如何与相关的回避子空间的特殊几何特性相关，并特别关注广义等级权重。通过这种方式，我们还可以在分散子空间上提供已知结果的替代性和简短证明。然后，我们使用这种简化的观点，以获得近MRD代码的几何表征，并在其最大长度上获得清晰的结合。最后，我们将准MRD代码的理论与$ h $散布的最大尺寸的子空间联系起来，并将其扩展到所有参数设置在MRD代码上已知的结果。
We revisit and extend the connections between $\mathbb{F}_{q^m}$-linear rank-metric codes and evasive $\mathbb{F}_q$-subspaces of $\mathbb{F}_{q^m}^k$. We give a unifying framework in which we prove in an elementary way how the parameters of a rank-metric code are related to special geometric properties of the associated evasive subspace, with a particular focus on the generalized rank weights. In this way, we can also provide alternative and very short proofs of known results on scattered subspaces. We then use this simplified point of view in order to get a geometric characterization of near MRD codes and a clear bound on their maximal length. Finally we connect the theory of quasi-MRD codes with $h$-scattered subspaces of maximum dimension, extending to all the parameters sets the already known results on MRD codes.
