格罗伯纳碱基和伽罗瓦环上的交替密码

2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060) Pub Date : 2000-06-25 DOI:10.1109/ISIT.2000.866746

E. Byrne, P. Fitzpatrick

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引用次数: 1

摘要

本文给出了一种求解伽罗瓦环R上交替码的Hamming度量译码问题的新算法。首先，我们发展了R|x/下标1/上的Grobner基的综合理论。，x/下标n/|，这是独立的兴趣。在单变量的情况下，我们证明了关键方程的解可以被确定为解模块的Grobner基中的某个最小元素。

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Grobner bases and alternant codes over Galois rings

We give a new algorithm for the solution of the Hamming metric decoding problem for alternant codes over a Galois ring R. First we develop a comprehensive theory of Grobner bases over R|x/sub 1/,...,x/sub n/|, which is of independent interest. By specialising to the case of one variable, we show that the solution of the key equation can be determined as a certain minimal element in a Grobner basis of the solution module.

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2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)

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