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

Hongwei Liu; Xu Pan

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arXiv · 2002.02165

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

Hongwei Liu·Xu Pan

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Abstract

In this paper, we first introduce the notion of generalized pair weights of an $[n, k]$-linear code over the finite field $\mathbb{F}_q$ and the notion of pair $r$-equiweight codes, where $1\le r\le k-1$. Some basic properties of generalized pair weights of linear codes over finite fields are derived. Then 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 $1\le r\le k-1$. Finally, a necessary and sufficient condition for a linear isomorphism preserving pair weights between two linear codes is obtained.

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Hongwei Liu, Xu Pan. 2020-02-06. Generalized Pair Weights of Linear Codes and Linear Isomorphisms Preserving Pair Weights. https://arxiv.org/abs/2002.02165

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