Generator matrix for linear block code

1. How do you write a generator matrix?
2. How do I find the code word in a generator matrix?

How do you write a generator matrix?

The transition matrix for the corresponding jump chain is given by P=[p00p01p10p11]=[0110]. Therefore, we have g01=λ0p01=λ,g10=λ1p10=λ. Thus, the generator matrix is given by G=[−λλλ−λ].

How do I find the code word in a generator matrix?

In general, if you have a code over F2 and a k×n generator matrix (that is, k≤n, n is the length of the code and k is the dimension.) then all of the codewords will be given by multiplying by the vectors from Fk2. Since there are 2k of these vectors, there will be 2k codewords.