Geodesic
On subspace designs
Paolo Santonastaso1; Ferdinando Zullo1
1Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy
EMS surveys in mathematical sciences, Volume 11 (2024) no. 1, pp. 1-62

See the original article notice from the EMS Press source

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.
DOI: 10.4171/emss/77
Classification: 05B99, 51E22, 51E23, 94B05
Keywords: Subspace design, subspace evasive subspace, s-design, MSRD code, scattered subspace, sum-rank metric code, cutting design, dimension expander

Paolo Santonastaso  1 ; Ferdinando Zullo  1

1 Università degli Studi della Campania “Luigi Vanvitelli”, Caserta, Italy 
Paolo Santonastaso; Ferdinando Zullo. On subspace designs. EMS surveys in mathematical sciences, Volume 11 (2024) no. 1, pp. 1-62. doi: 10.4171/emss/77
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