Strong Singleton type upper bounds for linear insertion-deletion codes

06/21/2021

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by   Hao Chen, et al.

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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.