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Decoding the extended binary Golay code by an iterative invert-one-bit scheme

In this paper, a new decoding algorithm of the extended binary Golay code is proposed. Based on the proposition developed in this paper, all probable patterns of occurred weight-4 error, which are always decoded to the same weight-3 error pattern, are determined from an iterative invert-one-bit scheme instead of the look-up table of weight-7 codewords. And the most possible one will be obtained by estimating the emblematic probability values of all probable patterns. The simulation result of this decoder in AWGN shows that more than 99% of four errors are corrected if Eb/N0 is greater than 5 dB.