How do you generate a parity check matrix? - Answers

In order to generate the parity check matrix you must first have the generator matrix and the codeword to check and see if it is correct. 1. Place your generator in row reduction form 2. Get the basis vectors 3. Put the vectors together to get the parity check matrix 4. Check it b multiplying the codewords by the parity = 0 For an example: 2*4 Generator Matrix [1 0 1 1 0 1 1 0] Rank = 2...therefore the number of columns is 2...Rank + X = # of columns of the Generator matrix v1+v3+v4 = 0 v2+v3 = 0 v1 = -r1-r2 v2 = -r1 v3 = r1 v4 = r2 Parity = [-1 -1 -1 0 1 0 0 1]