The insertion-deletion codes was motivated to correct the synchronization errors. In this paper we prove several Singleton type upper bounds on the insdel distance of linear codes insertion-deletion codes, based on 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 algebraic-geometric codes 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, 证明在线性代码插入删除代码的内侧距离上有几个单质型的上界。 我们的内界比以前已知的界限要强。 这些上界对坐标位置的任何固定定序有效。 我们将这些上界对一些双周期代码和带有任何坐标顺序的二进制 Reed- Muller 代码, 以及一些双进 Reed- Muller 代码和具有某些特殊协调顺序的代数- 地理界码 。