论文标题
在$ \ mathbb {z} _4 $上的广义准环境代码上
On generalized quasi-cyclic codes over $\mathbb{Z}_4$
论文作者
论文摘要
基于良好的代数结构和实践性，广义准环（GQC）代码在编码理论中起重要作用。在本文中，我们在$ \ mathbb {z} _4 $上研究了一些结果，包括归一化生成集，最小生成集和其双重代码的归一化生成集。作为一个应用程序，新的$ \ mathbb {z} _4 $ - 线性代码和良好的非线性二进制代码是从$ \ mathbb {z} _4 $的GQC代码构建的。
Based on good algebraic structures and practicabilities, generalized quasi-cyclic (GQC) codes play important role in coding theory. In this paper, we study some results on GQC codes over $\mathbb{Z}_4$ including the normalized generating set, the minimum generating set and the normalized generating set of their dual codes. As an application, new $\mathbb{Z}_4$-linear codes and good nonlinear binary codes are constructed from GQC codes over $\mathbb{Z}_4$.
