I really want to know how can we know if the code coming from this parity check matrix is systematic or not ?
Also, is there anyway to know the encoding rule (the order of which the message bit and parity bit are arranged) ?
For example m1 m2 m3 m4 p1 p2 p3 or m1 m2 p1 m3 p2 p3 m4 ?
I really think that I should try to put it back into a corresponding generator matrix by using some row and column operation but swapping column of H around would result in a completely different set of code from the original H. In some sense I have a feeling that some how I should keep track of the column permutation