  The insertion-deletion codes were motivated to correct the synchronization
errors. In this paper we prove several coordinate-ordering-free upper bounds on
the insdel distances of linear codes, which are based on the generalized
Hamming weights and the formation of minimum Hamming weight codewords. Our
bounds are stronger than some previous known bounds. We apply these upper
bounds to some cyclic codes and one algebraic-geometric code with any
rearrangement of coordinate positions. Some strong upper bounds on the insdel
distances of Reed-Muller codes with special coordinate-ordering are also given.
