序列综合与一类代数几何码的有效译码＊

Berlekamp-Massey算法是用来解决域上序列的综合问题。本文用多元多项式系数的齐次方程给出这个问题的新的数学模型。本文利用多项式理想论中的Grbner基理论,给出了上述模型的算法。此算法适用于环FX_1,…,X_n]中,当n=2时,就类似于Euclid算法。文中算法还可用于求解一类代数几何码的快速译码问题。

Synthesis of Sequences and Efficient Decoding for a Class of Algebraic Geometry Codes

The famous Berlekamp-Massey iteration algorithm is often used to give the solution of the synthesis problem of the sequence. In this paper, we present a more reasonable mathematical model, the linear homogeneous equations with polynomial coefficients, to describe the synthesis problem. The Grobner base theory in polynomial ring is used to present an efficient algorithm for the mathematical model. It turns out to be a generalization of Euclid's algorithm. The new algorithm can be used to deduce an efficient decoding for a class of algebraic geometry codes constructed by Justesen.