摘要： 局部修复码应用于分布式存储系统中，其码字的任意位发生错误都可通过读取该码字其他若干位予以修复。根据该特性，围绕三维、四维最优码展开研究，通过讨论已知特殊最优码的相关参数，同时分析已知最优码生成矩阵列向量之间的线性关系，使用矩阵变换、矩阵拼接、删截等方法，构造五元域上所有的三维、四维最优码。在此基础上，分析该码尽可能小的局部修复度，并通过C-M界判定局部修复度的最优性，得到距离最优的局部修复度。

关键词: 最优线性码, 有限域, Griesmer界, 生成矩阵, 局部修复度

Abstract: The local repair code is applied in distributed storage system.In this code,errors in any bit of code word can be repaired by reading other bits of the code word.According to this characteristic,the research is carried out around the three-dimensional and four-dimensional optimal codes.By discussing the relevant parameters of the known special optimal codes,analyzing the linear relationship between the column vectors of the generator matrix of the known optimal codes,and using matrix transformation,matrix concatenation,matrix subtraction and other methods,all the three-dimensional and four-dimensional optimal codes in the 5-ary domain are constructed.On this basis,the local repair degree of the code is analyzed as small as possible,and the optimal local repair degree of the code is determined by the C-M boundary,so as to obtain the local repair degree with optimal distance.

Key words: optimal linear code, finite field, Griesmer bound, generator matrix, local repair degree

中图分类号: 

• O157.4