Consider the following generator matrix for a $(7,4)$ linear block

code:

$G=\left[\begin{array}{ccccccc}0& 1& 1& 1& 0& 1& 0\\ 0& 0& 1& 0& 0& 1& 1\\ 0& 0& 0& 1& 1& 1& 0\\ 1& 0& 1& 1& 0& 0& 0\end{array}\right]$

a$.$ Express $G$ in a systematic form. Hint: you need to swap

rows and or perform rows addition $($add two or more rows$)$

until you get an $I_k$ matrix.

b$.$ List all valid code$-$words that could be generated by this

code.

c$.$ How many errors this code can detect, and at how many

error locations?

d$.$ How many errors this code can detect and correct?

Implement the syndrome table.