Chinese remainder codes

Abstract

Chinese remainder codes are constructed by applying weak block designs and the Chinese remainder theorem of ring theory. The new type of linear codes take the congruence class in the congruence class ring R/I₁ ∩ I₂ ∩ ··· ∩ I_n for the information bit, embed R/J_i into R/I₁ ∩ I₂ ∩ ··· ∩ I_n, and assign the cosets of R/J_i as the subring of R/I₁ ∩ I₂ ∩ ··· ∩ I_n and the cosets of R/J_i in R/I₁ ∩ I₂ ∩ ··· ∩ I_n as check lines. Many code classes exist in the Chinese remainder codes that have high code rates. Chinese remainder codes are the essential generalization of Sun Zi codes.

Keywords

block design / Chinese remainder theorem / error-correcting codes / Sun Zi codes / 13Hxx

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