If $A_j,j=0,1,2,$dotsdotsdots,$7$ defines the number of the codewords with hamming weight $j$ of

$(7,4)$ Linear block code. Given:

$A_0=1,A_1=A_2=A_5=A_6=0,A_4=7,A_7=1$

a$)$ Determine the $d_{\text{m}\text{i}\text{n}}$ of this code.

b$)$ Compute the probability of undetectable error patterns if the channel error probability is$.$

$0\mathrm{.}05?$