4. (a) Find the parity check matrix in systematic form for a code over Z5 capable of correcting single errors. Assume that the number of information bits, k=8. (b) Find the generator matrix for this code. (C) Suppose the given information word is (12041123). Find the corre- sponding codeword. (d) Suppose there is a single error in the fourth information digit which changed from 4 to 2. Explain how error correction is done. 4. (a) Find the parity check matrix in systematic form for a code over Z5 capable of correcting single errors. Assume that the number of information bits, k=8. (b) Find the generator matrix for this code. (C) Suppose the given information word is (12041123). Find the corre- sponding codeword. (d) Suppose there is a single error in the fourth information digit which changed from 4 to 2. Explain how error correction is done