Question:
Having code series ${a_{i}}$ where $i= 1,...,6$ and control groups:
$Z_{1} = a_{1},a_{2},a_{4}$
$Z_{2} = a_{3},a_{4},a_{6}$
$Z_{3} = a_{2},a_{5},a_{6}$
a) give numbers of information bits
b) designate(create) generator martix G
c) parity check H
My question:
I check on wikipedia and it says"every bits that's not power of 2 is information bit" so I guess information bits are $a_{3}, a_{5} , a_{6}$ so there would be mine information bits but how do I create generator matrix $G$ and parity check matrix $H$?
Any help would be appreciated.
To find $G$: find some code words that will form a basis for your code (you should be able to find the dimension of the code so you know how many you need), put them in as rows of the matrix $G$.
To find $H$: You should have a theorem that tells you, after row reducing $G$ to have the form $\begin{bmatrix} I & A \end{bmatrix}$, there is a way to use $A$ to get the matrix $H$.