What will be the Generator Matrix for 4B/5B Linear Block code?

Question

From the 4B/5B encoding scheme dataward 0000 in encoded to 11110 codeword similarly 0001 is encoded to 01001, etc.

Here the result of XOR operation between two codewords will be another valid codeword.

I should multiply the data word with the a generator matrix. But what will be the actual generator matrix in this case?

Here the parity matrix has only one column. How can I produce it?

I search google and study books too. But everywhere they are telling only the same thing but I did not get my answer.

Answer 1

I should multiply the data word with the a generator matrix. But what will be the actual generator matrix in this case?

The "generator matrix" makes only sense for linear error correcting codes. This is not a linear code. For one thing, in a linear code the zero input is mapped to the zero codeword. Besides, (assuming we are speaking of a binary linear code), the allowed inputs (raw messages) should correspond to the $2^k=16$ binary tuples, but here you additional inputs (the "control sequences"). This does not even seem to be a code in the sense of ECC (error correcting codes), this is rather a line code. Quite a different concept.

Perhaps you are confusing "line code" with "linear code"?

BTW: I don't know why you call this a "Hamming code".