I just finished learning some basic concepts about Hamming code. Now I see this extended Hamming code and they say that you can "detect" up to 3 bits of error. Now, say, my actual codeword was $X=10100011$ and I received $Y=10011011$ (3 bits of error) and my transpose of parity check matrix $H(t)$ is below
1110 0111 1101 1011 1000 0100 0010 0001
Now from the rule I understand in (7,4) Hamming code was to compute syndrome which in this case would be S=1111 which is not present in the parity check matrix so that is probably not correct. So, can someone guide me with an example on how to detect 3 bit error per code in (8,4) Hamming code?