摘要
本文利用弱区组设计和环论中的“中国剩余定理”构造了中国剩余码。这种新型线性码是将同余类环 R/I_1∩I_2∩…∩I_n中的同余类作为信息位,将 R/J_i嵌入 R/I_1∩I_2∩…∩I_n,视其为R/I_1∩I_2∩…∩I_n的子环,R/J_i在R/I_1∩I_2∩…∩I_n中的陪集作为监督维线。中国剩余码中存在一系列码率较高的码类,它是孙子码的本质推广。
Chinese remainder codes are constructed by applying the weak block design and
Chinese remainder theorem of ring theory. The new type of linear codes are to take the con-
gruence class in the congruence class ring R/I_1∩I_2∩…∩I_n for the information bit, to em-
bed R/J_i into R/I_1∩I_2∩…∩I_n as a subring of R/I_1∩I_2∩…∩I_n, and to regard the
cosets of R/J_i in R/I_1∩I_2∩…∩I_n as check lines. There exist many code classes in chinese
remainder codes, which have higher code rate. Chinese remainder codes are essential gener-
alization of Sun Zhi codes.
关键词
线性码
同余类
陪集
环
linear code
congruence class
coset
ring
