Walsh函数在解二元域方程组上的应用

The Application of Walsh Function in Resolving of F(2) equations

本文从分析二元域上的方程的解出发，探讨了二元域上向量乘法矩阵与Ｗａｌｓｈ矩阵的关系，从而推导出利用Ｗａｌｓｈ变换求解二元域上方程组的方法，并进一步推广到方程组中含有错误方程的情况，成功地解决了含错方程组的解法问题．在分析分组码、卷积码的校验多项式以及移位寄存器序列的生成多项式中有很好的实用价值．

This paper analyzes the solutions of F(2) equations, discusses the relation between Walsh matrix and matrix of vector multiplication in F(2), developed a algorithm for resolving F(2) equations with Walsh trans- form. This algorithm can resolve F(2) equations with error equations . This algorithm can be applied in analyzing block code, convolutional code and shift register sequence,