中国剩余码

Chinese Remainder Codes

中文关键词:  线性码  同余类  陪集  环

英文关键词:linear code  congruence class  coset  ring

中文摘要:

      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/I₁∩I₂∩…∩I_n中的同余类作为信息位,将 R/J_i嵌入 R/I₁∩I₂∩…∩I_n,视其为R/I₁∩I₂∩…∩I_n的子环,R/J_i在R/I₁∩I

英文摘要:

      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/I₁∩I₂∩…∩I_n for the information bit, to em- bed R/J_i into R/I₁∩I₂∩…∩I_n as a subring of R/I₁∩I₂∩…∩I_n, and to regard the cosets of R/J_i in R/I₁∩I₂∩…∩I_n as check lines. There exist many code classes in chinese remainder codes, which have higher code rate. Chinese remainder codes are essential generalization of Sun Zhi codes.