在分布式存储系统中，当一个存储节点失效时，需要通过其它一些存储节点的数据来修复失效节点的数据，通常可以通过分布式存储编码来实现。局部修复码是一类重要的分布式存储编码，广泛应用于分布式存储系统中。局部修复码是信息论和编码理论领域中一个重要的研究课题。本课题综合利用信息论、编码理论、组合数学的方法研究局部修复码的构造、性能分析和译码算法，给出达到Singleton界的最优局部修复码的新的构造方法，推导局部修复码的新的简洁的理论界，给出达到新的理论界的最优局部修复码的构造方法，设计循环和常循环的最优局部修复码的构造方法和译码算法。根据实际应用中的不同需求，建立新的局部修复码的数学模型，给出新的局部修复码模型的理论分析和具体构造。这项研究的进展将丰富局部修复码的理论，提高分布式存储系统的效率和可靠性能，促进我国信息编码技术和信息存储技术的发展。

In distributed storage systems, when a storage node fails, we usually recover its data from the data stored in some other storage nodes. This is usually done by coding for distributed storage. Locally repairable codes is an important class of coding for distributed storage, and has been widely used in distributed storage systems. Locally repairable codes is an important research topic in information theory and coding theory. In this project, by using methods from information theory, coding theory and combinatorics, we study the construction methods, performance analysis and decoding algorithm of locally repairable codes. We study and give constructions of new optimal locally repairable codes meeting the Singleton type bound. We will present new and explicit bounds on locally repairable codes, and construct new optimal locally repairable codes meeting these new bounds. We will design the construction methods and decoding algorithms for cyclic and contacyclic optimal locally repairable codes. Based on the application background, we establish the new mathematical model of locally repairable codes, and present the bounds and constructions for this new type of locally repairable codes. The research progress of this project will enrich the theory of locally repairable codes, and enhance the efficiency and reliability of distributed storage systems, and promote the development of information coding technology and information storage technology in China.