The Hamming(7,4) forward error correction code encodes 4 data payload bits into a 7-bit codeword by appending 3 parity check bits. With a minimum Hamming distance d_min = 3 between valid codewords, the receiver calculates a 3-bit syndrome vector S = H · r^T to locate any single-bit transmission error, instantly flipping and correcting the corrupted bit without retransmission.