TL;DR
This paper explores the properties and bounds of subspace designs, providing explicit constructions, and connects them to sum-rank metric codes, with applications in combinatorics and coding theory.
Contribution
It establishes tight bounds for subspace designs, introduces explicit constructions, and links them to sum-rank metric codes and various combinatorial structures.
Findings
Bounds involving subspace design parameters are tight.
Explicit constructions of subspace designs are provided.
Connections to sum-rank metric codes and applications in combinatorics are demonstrated.
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.
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