标题： 具有任意维数船体的线性码和纯LCD码 显示英文标题

标题： Linear codes with arbitrary dimensional hull and pure LCD code

摘要： 本文介绍了一种由任意非LCD码构造具有小维数 hull 的线性码的一般方法。此外，我们证明了对于任意维数为$dim(Hull(\Co))=h$的$\F_q$（$q > 3$）上的线性码$\Co$，存在一个与之等价的线性码$\Co_j$，其 hull 维数为$dim(Hull(\Co_j))=j$，其中$0\leq j \leq h$为任意整数。我们还引入了纯LCD码的概念；即一个LCD码及其所有等价码均为LCD码，并构造了一个无限族的纯LCD码。另外，我们还介绍了一类具有一维 hull 的线性码的一般构造方法。 显示英文摘要

摘要： In this paper, we introduce a general construction of linear codes with small dimension hull from any non LCD codes. Furthermore, we show that for any linear code $\Co$ over $\F_q$ ($q > 3$) with $dim(Hull(\Co))=h$ there exist an equivalent codes $\Co_j$ with $dim(Hull(\Co_j))=j$ for any integer $0\leq j \leq h$. We also introduce the notion of pure LCD code; an LCD code and all its equivalent are LCD; and construct an infinite family of pure LCD codes. In addition, we introduce a general construction of linear codes with one dimension hull.