In this paper we study geometric aspects of codes in the sum-rank metric. We establish the geometric description of generalised weights, and analyse the Delsarte and geometric dual operations. We establish a correspondence between maximum sum-rank distance codes and h-designs, extending the well-known correspondence between MDS codes and arcs in projective spaces and between MRD codes and h-scatttered subspaces. We use the geometric setting to construct new h-designs and new MSRD codes via new families of pairwise disjoint maximum scattered linear sets.

翻译：本文研究和秩度量中的码的几何性质。我们建立了广义权重的几何描述，并分析了Delsarte对偶与几何对偶运算。通过将最大和秩距离码与h-设计对应起来，我们推广了MDS码与射影空间中的弧、MRD码与h-分散子空间之间的已知对应关系。利用几何框架，我们通过构造新的两两不相交最大分散线性集族，得到了新的h-设计与新的MSRD码。