On subspace designs

Paolo Santonastaso; Ferdinando Zullo

doi:10.4171/emss/77

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arXiv · 2204.13069

On subspace designs

Paolo Santonastaso·Ferdinando Zullo

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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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Paolo Santonastaso, Ferdinando Zullo. 2022-04-27. On subspace designs. https://doi.org/10.4171/emss/77

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