Discrete structure

We use the Hamming code H_3. Four codewords c_1, c_2, c_3, c_4 are transmitted one after another over a noisy channel to obtain the words w_1, w_2, w_3, w_4, respectively. Each transmission of a codeword c_i, for 1 lessthanorequalto i lessthanorequalto 4, results in at most one error, in that at most one bit gets flipped. The words w_i, for 1 lessthanorequalto i lessthanorequalto 4, obtained on the other end of the channel, are as follows: w_1 = 1 1 1 1 1 1 1 1 w_2 = 1 1 1 0 0 1 1 w_3 = 1 1 0 1 1 0 1 w_4 = 1 0 1 0 1 0 1 Decode the words w_1, w_2, w_3, w_4 to obtain the original transmitted codewords c_1, c_2, c_3, c_4