Linear codes have a wide range of applications in the data storage systems, communication systems, consumer electronics products since their algebraic structure can be analyzed and they are easy to implement in hardware. How to construct linear codes with excellent properties to meet the demands of practical systems becomes a research topic, and it is an efficient way to construct linear codes from cryptographic functions. In this paper, we will introduce some methods to construct linear codes by using cryptographic functions over finite fields and present some recent results and problems in this area.

中文翻译：

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利用密码函数构造线性码的最新结果和问题

线性代码由于可以分析其代数结构并且易于在硬件中实现，因此在数据存储系统，通信系统，消费电子产品中具有广泛的应用。如何构造具有优良性能的线性代码以满足实际系统的需求已成为研究的课题，它是从密码函数构造线性代码的有效途径。在本文中，我们将介绍一些通过在有限域上使用密码函数构造线性代码的方法，并介绍该领域的一些最新结果和问题。