New Complete Decoding of Triple-Error-Correcting Binary BCH Codes

Feng Gui-liang

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New Complete Decoding of Triple-Error-Correcting Binary BCH Codes

更新时间：2025-12-08

- New Complete Decoding of Triple-Error-Correcting Binary BCH Codes
- Acta Electronica Sinica Issue 2, Pages: 17-25(1986)
- 作者机构：
  
  上海计算技术研究所
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：1986
- 稿件说明：
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[1]冯贵良.纠三个错的二元BCH码的新的完全译码[J].电子学报,1986(02):17-25.

Feng Gui-liang. New Complete Decoding of Triple-Error-Correcting Binary BCH Codes[J]. Acta Electronica Sinica, 1986, (2): 17-25.
[1]冯贵良.纠三个错的二元BCH码的新的完全译码[J].电子学报,1986(02):17-25. DOI：

Feng Gui-liang. New Complete Decoding of Triple-Error-Correcting Binary BCH Codes[J]. Acta Electronica Sinica, 1986, (2): 17-25. DOI：

摘要

本文给出了求解一类非线性方程组的根的新方法。这类非线性方程组出现在纠三个错的二元BCH码的Van der Horst和Berger的完全译码中。当m是偶数时

长n=2

-1的纠三个错的二元BCH码的新的完全译码

只需要寻找二次方程的根以及最多m次计算GF（2）上m元矢量的内积。因而新的完全译码非常简单

并对中等大的m也很实用。

Abstract

A new method is given for finding out roots of one type of nonlinear equations

which appears in Van der Horst and Berger’s Complete decoding of triple-error-correcting binary BCH codes. When m is even

the new complete decoding of triple-error-correcting binary BCH codes with n = 2m - 1 requires only extracting the roots of quadratic equations and calculating at most m times inner products of m-dimensional vectors over GF（2）. The new complete decoding is very simple

and can be realized in practice even for moderate m.

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