On MSRD codes, h-designs and disjoint maximum scattered linear sets
Information Theory
2023-08-02 v1 Combinatorics
math.IT
Abstract
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.
Cite
@article{arxiv.2308.00378,
title = {On MSRD codes, h-designs and disjoint maximum scattered linear sets},
author = {Paolo Santonastaso and John Sheekey},
journal= {arXiv preprint arXiv:2308.00378},
year = {2023}
}