On subspace designs
Information Theory
2023-11-15 v2 Combinatorics
math.IT
Abstract
Guruswami and Xing introduced subspace designs in 2013 to give the first construction of positive rate rank metric codes list-decodable beyond half the distance. In this paper we provide bounds involving the parameters of a subspace design, showing they are tight via explicit constructions. We point out a connection with sum-rank metric codes, dealing with optimal codes and minimal codes with respect to this metric. Applications to two-intersection sets with respect to hyperplanes, two-weight codes, cutting blocking sets and lossless dimension expanders are also provided.
Cite
@article{arxiv.2204.13069,
title = {On subspace designs},
author = {Paolo Santonastaso and Ferdinando Zullo},
journal= {arXiv preprint arXiv:2204.13069},
year = {2023}
}