Consider the following block code: C $=\{(000000),(010101),(101010),(111111)\}.$

$($a$)$ Is the code linear? Explain.

$($b$)$ What is the minimum Hamming distance for this code?

$($c$)$ For a BSC channel with uncoded error$-$rate p $=10-3,$ what is the codeword error probability for

this code?