论文标题
具有两个或三个权重的线性代码的构造，来自矢量双弯曲函数
Constructions of linear codes with two or three weights from vectorial dual-bent functions
论文作者
论文摘要
具有几个权重的线性代码是编码理论中重要的一类代码，并且引起了很多关注。在本文中，我们介绍了$ q $ - ary线性代码的几种结构，其中有两个或三个权重的矢量双弯曲函数，其中$ q $是奇数prime $ p $的功率。完全确定了构建的$ Q $ - ARY线性代码的重量分布。我们说明文献中的一些已知构造可以通过我们的构造获得。在某些特殊情况下，我们构造的线性代码可以符合Griesmer的界限。此外，根据构建的$ Q $ - ARY线性代码，我们获得具有有趣访问结构的秘密共享方案。
Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial dual-bent functions, where $q$ is a power of an odd prime $p$. The weight distributions of the constructed $q$-ary linear codes are completely determined. We illustrate that some known constructions in the literature can be obtained by our constructions. In some special cases, our constructed linear codes can meet the Griesmer bound. Furthermore, based on the constructed $q$-ary linear codes, we obtain secret sharing schemes with interesting access structures.
