Top:coding Theory be a linear $n,k-$code. We have seen many examples where the

first $k$ bits of every codeword are the message bits. However, this condition

is not necessary. An information set for $C$ is any set $S$ of $k$ linearly inde$-$

pendent columns of a generator matrix for $C.$ It turns out that any such

set $S$ can define the placement of the code's message bits. For example, if

$S=\{co{l}_1,co{l}_3,co{l}_4,co{l}_6\}$ is an information set for $C,$ then one can choose the

$1$ st$,3$rd$,4$ th and $6$ th bits as the message bits of its codewords.

Let $C$ be the binary $6,4-$code with generator matrix given by

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

Which of the following sets are information sets for $C?$