Linear algebra help

A 4 bit message b = [b_1, b_2, b_3, b_4] is to be sent via a noisy channel. Three parity bits are employed p_1 = (b_1 + b_2 + b_4) mod 2, p_2 = (b_1 + b_3 + b_4) mod 2 and p_3 = (b_2 + b_3 + b_4) mod 2. The message plus parity bits is sent as a 7 bit message c = [c_1, ..., c_7] where c_1 = p_1, c_2 = p_2, c_3 = b_1, c_4 = p_3, c_5 = b_2, c_6 = b_3 and c_7 = b_4. If the message received at the destination is C_rec = [0, 1, 0, 1, 1, 0, 0], what was the original 4 bit message? Assume that there can be at most one erroneous bit