Generalized Pair Weights of Linear Codes and Linear Isomorphisms Preserving Pair Weights

摘要

In this paper, we introduce the notion of generalized pair weights of an [n, k]-linear code over the finite field F-q and the notion of pair r-equiweight codes, where 1 <= r <= k - 1. Some basic properties of generalized pair weights of linear codes over finite fields are derived. We obtain a necessary and sufficient condition for an [n, k]-linear code to be a pair equiweight code, and we characterize pair r-equiweight codes for any 1 <= r <= k - 1. A necessary and sufficient condition for a linear isomorphism to preserve pair weights between two linear codes is obtained. At the end of this paper, an application of generalized pair weights of linear codes to symbol-pair read wire-tap channels of type II is introduced.

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