In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear subspace-metric codes and linear subset-metric codes are proved. Subspace distances and subset distances of codes are natural lower bounds for insdel distances of codes, and then can be used to lower bound the insertion-deletion error-correcting capabilities of codes. Our subspace-metric codes or subset-metric codes can be used to construct explicit well-structured insertion-deletion codes directly. $k$-deletion correcting codes with rate approaching $1$ can be constructed from subspace codes. By analysing the subset distances of folded codes from evaluation codes of linear mappings, we prove that they have high subset distances and then are explicit good insertion-deletion codes.

翻译：在本文中,我们根据子空间编码,引入了子空间计量码和子计量码。它们是协调位置独立伪数,适合折叠代码。线性次空间计量码和线性子计量码的半星际上界得到了证明。分空间距离和代码的子范围距离是代码内分距的自然较低界限,然后可用于降低代码的插入-删除错误校正能力。我们的子空间计量码或子计量码可以直接用于构建明确的结构完善的插入-删除代码。可以用子空间编码来构建比例接近1美元的半星际校正码。通过分析线性绘图评价码的折叠码的子范围距离,我们证明它们具有高子距离,然后是明确的插入-删除代码。