Reed-solomon Code, Multi-cycle Coding Algorithm

In this paper, we introduce the method of Grobner bases and the method of Wu characteristic set, which allow us to solve the problem of solving polynomial equations. And we give their algorithm on the computer.Based on studying the algorithms to solve the problem of solving polynomial of generator of polynomial ideals, and analysis the structural characteristics of the coding algorithm of a weight cycle code and multiple cycle code (Reed-Solomon codes), we give an algorithm which base on the method of Wu characteristic set for multi-cycle codes.The basic concept and the basic properties of the linear code to be described. Based on the Grobner bases method is used to seek the generators of zero-dimensional ideal, we introduce the method of Grobner bases, which used for the coding algorithm of multi-cycle of Reed-Solomon code (RS code).We show that another useful property of the zero-dimensional polynomial ideal which generated by polynomial equations ,of which Wu characteristic set is a generator of this ideal of Groebner basis . Based on the prove, we give an coding algorithm of multiple cycle RS codes. Some direct application of our note are also illustrated.