The insertion-deletion codes was motivated to correct the synchronization errors. In this paper we prove several Singleton type upper bounds on the insdel distances of linear insertion-deletion codes, based on the generalized Hamming weights and the formation of minimum Hamming weight codewords. Our bound are stronger than some previous known bounds. These upper bounds are valid for any fixed ordering of coordinate positions. We apply these upper bounds to some binary cyclic codes and binary Reed-Muller codes with any coordinate ordering, and some binary Reed-Muller codes and one algebraic-geometric code with certain special coordinate ordering.

翻译：插入删除代码的动机是纠正同步错误。 在本文中, 我们根据普通的 Hamming 重量和最小的 Hamming 重量编码的形成, 证明在线性插入删除代码的离心距离上有几个单列通型的上限。 我们的绑定比以前已知的界限要强。 这些上限对坐标位置的任何固定顺序有效。 我们将这些上限适用于某些双周期代码和带有任何坐标顺序的二进制 Reed- Muller 代码, 一些二进制 Reed- Muller 代码, 以及一个带有某些特殊坐标顺序的代数- gebraic- geolog 代码 。