A necessary condition for the existence of a set ofJorthogonal parity check equations is developed, and it is demonstrated that, except for the trivial codes, the Reed-Solomon codes are notL-step orthogonalizable. Massey's concept of threshold decoding is generalized, and it is demonstrated that the Reed-Solomon codes are completely threshold decodable. Since every BCH code is a subcode of some Reed-Solomon code, every BCH code has a generalized threshold decoder.
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W. Gore (1969) studied this question.
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