
Parity Check Matrix
I have this example with the answer, but I’m sure the way I use to find the Parity Check Matrix is correct. So please help me along, if I’m wrong.
Example, the generator matrix for a [7,4] linear block code is given as
 1 0 0 0 1 0 1 
 0 1 0 0 1 1 1 
 0 0 1 0 0 1 0  = G
 0 0 0 1 0 1 0 

Am I correct that G is the first 4 bit and P is the last 3 bit because of the [7, 4]???
Is it the same for [5, 3], G is the first 3 bit???
 1 0 0 0 1 0 1 
 0 1 0 0 1 1 1 
 0 0 1 0 0 1 0  = G
 0 0 0 1 0 1 0 
___G____P_
If is correct, I have the P and can compute P^t.
 1 0 1 
 1 1 1 
 0 1 0  = P
 0 1 0 
So
 1 1 0 0 
 0 1 1 1  = P^t
 1 1 0 0 
The Parity Check Matrix formula I’m given is H = [P^t  I]
So I take the P^t and add on with I behind. Which the result is:
 1 1 0 0 1 0 0 
 0 1 1 1 0 1 0  = H
 1 1 0 0 0 0 1 
__P^t____I_
But where did the ‘–‘P^t go to??
As my given answer is this, without the ‘–‘.
I’m not sure how did the I come from but it looks like a method by putting a bit at a time.
Lot of help
Ken JS
