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.
On subspace designs / Santonastaso, Paolo; Zullo, Ferdinando. - In: EMS SURVEYS IN MATHEMATICAL SCIENCES. - ISSN 2308-2151. - 11:1(2023), pp. 1-62. [10.4171/emss/77]
On subspace designs
Santonastaso, Paolo;
2023
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
