A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications
A Simple Proof of Horiguchi's Error-Value Formula in Decoding of Alternant Codes and Its Applications
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DOI：
10.1587/transfun.e92.a.2146
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发表时间：
2009-08
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影响因子：
--
通讯作者：
H. Matsui
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文献类型：
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作者：
H. Matsui
给出了Horiguchi交替码误差值公式的一个直接的简短证明。Horiguchi公式只使用Berlekamp-Massey算法的输出多项式，比用于译码交替码的扩展欧几里德算法具有更小的计算复杂度。作为证明的一个应用，我们给出了交替码及其单扩展码和双扩展码的生成矩阵和校验矩阵的显式表达式。
A direct short proof of Horiguchi's formula for error values in alternant codes is provided. Horiguchi's formula employs only output polynomials of Berlekamp-Massey algorithm, which has less computational complexity than extended Euclidean algorithm for decoding alternant codes. As an application of our proof, we provide an explicit formula for the generator and parity check matrices of alternant codes and their singly- and doubly-extended codes.