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Chinese remainder codes. (English) Zbl 1222.94044

Front. Math. China 1, No. 3, 452-461 (2006); translation from J. Math. Res. Expo 24, No. 2, 347-352 (2004).
This is a translation from [J. Math. Res. Expo. 24, No. 2, 347–352 (2004; Zbl 1054.94016)].
Summary: 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 congruence class in the congruence class ring \(R/I_1\cap I_2\cap\cdots\cap I_n\) for the information bit, to embed \(R/J_i\) into \(R/I_1\cap I_2\cap\cdots\cap I_n\) as a subring of \(R/I_1\cap I_2\cap\cdots\cap I_n\), and to regard the cosets of \(R/J_i\) in \(R/I_1\cap I_2\cap\cdots\cap I_n\) as check lines. There exist many code classes in Chinese remainder codes which have a higher code rate. Chinese remainder codes are an essential generalization of Sun Zhi codes.

MSC:

94B25 Combinatorial codes
13A15 Ideals and multiplicative ideal theory in commutative rings

Citations:

Zbl 1054.94016
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References:

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