Q$4$: The generated matrix for a binary LBC is given by: $(25$M$)$

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

a$)$ Use Hamming bounds to find error correction capability.

b$)$ Find parity check matrix.

c$)$ Find codeword table and Hamming weight. Then compute the error correction capability and compare with point $($a$).$

d$)$ Find the corrected word if the received word is $[101111001]$