Constructions of Linear Codes With One-Dimensional Hull
Constructions of Linear Codes With One-Dimensional Hull
复制标题
具有一维外壳的线性码的构造
DOI：
10.1109/tit.2018.2863693
复制
发表时间：
2019
影响因子：
2.5
通讯作者：
Zeng Peng
中科院分区：
文献类型：
--
作者：
Li Chengju;Zeng Peng
线性码的壳被定义为码与其对偶的交，最初是用来对有限射影平面进行分类的。在判定两个线性码的置换等价性的算法的复杂度和计算一个线性码的自同构群时，外壳起着重要的作用。研究表明，在船体尺寸较小的情况下，这些算法是非常有效的。本文的目的是给出线性码和循环码具有一维壳的一些充要条件。结果表明，不存在这样的二进制或三元循环码。在此基础上，利用二次数域、部分差集和差集，给出了具有一维壳的线性码的一些构造。我们还利用一维壳构造了循环码。得到了一些具有一维壳的最优码。
The hull of a linear code is defined to be the intersection of the code and its dual, and was originally introduced to classify finite projective planes. The hull plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code. It has been shown that these algorithms are very effective in general if the size of the hull is small. The objective of this paper is to present some sufficient and necessary conditions that linear codes and cyclic codes have one-dimensional hull. It is shown that there are no such binary or ternary cyclic codes. Based on these characterizations, some constructions of linear codes with one-dimensional hull were given by employing quadratic number fields, partial difference sets, and difference sets. We also construct cyclic codes with one-dimensional hull. Some optimal codes with one-dimensional hull are obtained.