Decoder malfunction in BCH decoders

A t-error-correcting bounded-distance decoder either produces the codeword nearest the received vector (if there is a codeword at distance no more than t) or indicates that no such codeword exists. However, BCH decoders based on the Peterson-Gorenstein-Zierler algorithm or the Euclidean algorithm can malfunction and produce output vectors that are not codewords at all. For any integer i no greater than t/2, if the received vector is at distance at most t-2i from a codeword belonging to a (t-i)-error-correcting BCH supercode, then the BCH decoder output is that codeword from the supercode.<
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