A message-passing iterative decoding method of an associated LFSR sequence (or M-sequence) as a simplex code, to a parity matrix H. The method includes determining a set of parity polynomials with a low weight obtained by combining the parity equations of the matrix H. For each combination of K such polynomials of this set, an extended parity matrix Hext is built by concatenating elementary parity matrices associated with the parity polynomials of said combination. The combination of parity polynomials leading to a bipartite graph not having cycles with a length 4 and having a minimum number of cycles with lengths 6 and 8 is selected. Then, the LFSR sequence is decoded using the bipartite graph corresponding to the selected combination. This decoding method enables the false-alarm rate to be substantially reduced.