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.

翻译：Guruswami和Xing于2013年引入子空间设计，首次构建了超越半数距离可列表解码的正速率秩度量码。本文给出了子空间设计参数的相关界，并通过显式构造证明其紧致性。我们指出了子空间设计与和秩度量码之间的联系，探讨了该度量下的最优码与最小码。此外，还提供了子空间设计在超平面双交集、双重量码、切割阻塞集及无损维数扩展器等领域的应用。