On the Solution of Algebraic Equations over Finite Fields
On the Solution of Algebraic Equations over Finite Fields
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发表时间：
2004
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通讯作者：
É.;R.;Berleka
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作者：
É.;R.;Berleka
本文通过求解某些代数方程，给出了快速解码某些纠错码的新方法。正如Peterson（1961）所描述的，特征为p的域上的Bose-Chaudhuri Hocquenghem码的位置与扩展域GF（pk）的元素相关。代码的设计方式是，通过对接收到的字进行适当选择的奇偶校验，可以直接获得错误位置的加权幂和对称函数。Berlekamp（1967）提出了由加权幂和对称函数计算初等对称函数的好方法。初等对称函数，a1 a2，…， at为根为误差位置的代数方程的系数
This article gives new fast methods for decoding certain errorcorrecting codes by solving certain algebraic equations. As described by Peterson (1961), the locations of a Bose-Chaudhuri Hocquenghem code over a field of characteristic p are associated with the elements of an extension field, GF(pk). The code is designed in such a way that the weighted power-sum symmetric functions of the error locations can be obtained directly by computing appropriately chosen parity checks on the received word. Good methods for computing the elementary symmetric functions from the weighted power-sum symmetric functions have been presented by Berlekamp (1967). The elementary symmetric functions, a l , a2, .. , at are the coefficients of an algebraic equation whose roots are the error locations