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

作者：Liu, Hongwei; Pan, Xu^*

来源：IEEE Transactions on Information Theory, 2022, 68(1): 105-117.

DOI：10.1109/TIT.2021.3120229

• Generalized pair weights
• pair equiweight codes
• pair r-equiweight codes
• linear isomorphisms to preserve pair weights

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.