Consider the binary code with the $P$ matrix

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

$($i$)$ Is the word $)$ is a code word? A code word is of the form $($X $11100).$ Is X a $0$

or $1?$

$($ii$)$ Suppose the code word $(001111)$ is transmitted, but $(001101)$ is received. What is

the resultant syndrome? Where would this syndrome indicate an error had occurred?

$($iii$)$ How many code words are in this code? List them.

$($iv$)$ What is the smallest number of errors that could change one code word into another code

word?