论文标题
线性代码和线性同构的一般对重量保留对重量的权重
Generalized Pair Weights of Linear Codes and Linear Isomorphisms Preserving Pair Weights
论文作者
论文摘要
在本文中，我们首先介绍了有限字段$ \ mathbb {f} _q $的$ [n，k] $ - 线性代码的广义对权重的概念和一对$ r $ - equigiight代码的概念，其中$ 1 \ le r \ le r \ le r \ le r \ le r \ le r \ le k-1 $。得出了有限场上线性代码的一般对权重的一些基本特性。然后，我们获得了$ [n，k] $ - 线性代码作为一对优量代码的必要条件，并且我们对任何$ 1 \ le R \ le r \ le l le k-1 $的Pair $ r $ equiweight代码进行表征。最后，获得了两个线性代码之间的对线性同构的必要条件。
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.
