On MSRD Codes, h‐Designs and Disjoint Maximum Scattered Linear Sets
Paolo Santonastaso, John Sheekey · Journal of Combinatorial Designs · 2025
ABSTRACT In this paper, we construct new optimal subspace designs and, consequently, new optimal codes in the sum‐rank metric. We construct new 1‐designs by finding sets of disjoint maximum scattered linear sets, and use these constructions to also find new ‐designs for . As a means of achieving this, we establish a correspondence between the metric properties of sum‐rank metric codes and the geometric properties of subspace designs. Specifically, we determine the geometric counterpart of the coding‐theoretic notion of generalised weights for the sum‐rank metric in terms of subspace designs and determine a geometric characterisation of MSRD codes. This enables us to characterise subspace designs via their intersections with hyperplanes and via duality operations.