JournalsemssVol. 11, No. 1pp. 1–62

On subspace designs

  • Paolo Santonastaso

    Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy

  • Ferdinando Zullo

    Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy
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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.

Cite this article

Paolo Santonastaso, Ferdinando Zullo, On subspace designs. EMS Surv. Math. Sci. 11 (2024), no. 1, pp. 1–62

DOI 10.4171/EMSS/77