Hamming (7,4) Encoder: This core encodes every 4-bit message into 7-bit codewords in such a way that the decoder can correct any single-bit error.
The encoder uses the generator matrix:
G=[ 1110000
1001100
0101010
1101001]
The codewords are generated by
C = M * G
where M=[m1 m2 m3 m4] is the 4-bit message.