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An approach to fast maximum likelihood decoding of some binary codes is presented. The binary codewords are regarded as images of some C/sub g/ group code, called the projected code, defined over an Abelian group A. The neighbourhood of z, z/spl isin/A/sup N/, the vector of symbol-by-symbol soft decoding, is examined to identify the most likely codeword of C/sub g/. A small list of candidate codewords is prepared by employing certain elimination rules. A substantial reduction of computational complexity is achieved by this method.