Considering (7,4) and (15, 11) Hamming codes.
Is there an intuitive idea why (15,11) performs better than (7, 4) in AWGN?
Is there anything to do with code rate?
The following curves show BER (bit error rate) versus Eb/No (energy of bit per noise density) of AWGN channel. It is possible to see that when bit has more energy (for fixed No), Hamming (15,11) performs better than (7,4), but the two codes can correct 1 bit.