$4$ Let $C_3$ be the binary $(2-$ry$)$ linear codes with generator matrix

$S_3\left[\begin{array}{ccccc}1& 1& 1& 1& 0\\ 0& 0& 1& 1& 1\end{array}\right]$

a $$ Construct a linear code $C_3$ by using $S_3$ in MAGMA programming language.

$b$ List all codewords and find the minimum distance of $C_3$ in MAGMA.

c $-$Use syndrome decoding to decode $11111$ in MAGMA.