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Berlekamp–Welch algorithm
The Berlekamp–Welch algorithm, also known as the Welch–Berlekamp algorithm, is named for Elwyn R. Berlekamp and Lloyd R. Welch. The algorithm efficiently corrects errors in BCH codes and Reed–Solomon codes (which are a subset of BCH codes). Unlike many other decoding algorithms, and in correspondence with the code-domain Berlekamp–Massey algorithm that uses syndrome decoding and the dual of the codes, the Berlekamp–Welch decoding algorithm provides a method for decoding Reed–Solomon codes using just the generator matrix and not syndromes.
==History on decoding Reed–Solomon codes==
# In 1960, Peterson came up with an algorithm for decoding BCH codes.〔. Previous publisher McGraw–Hill, New York, NY.〕 His algorithm solves the important second stage of the generalized BCH decoding procedure and is used to calculate the error locator polynomial coefficients that in turn provide the error locator polynomial. This is crucial to the decoding of BCH codes.
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抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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