Find a data to be transmitted with Hamming(7,4) if given data bits : 1010.
$a_1=a_3\oplus a_5\oplus a_7=1\oplus0\oplus0=1$
$a_2=a_3\oplus a_6\oplus a_7=1\oplus1\oplus0=0$
$a_3=a_5\oplus a_6\oplus a_7=0\oplus1\oplus0=1$
\begin{eqnarray} a_1&a_2&a_3&a_4&a_5&a_6&a_7\\ 1&0&1&1&0&1&0 \end{eqnarray}
Is it correct answer?
Well, it all depends on the generator matrix, say $$G =\left(\begin{array}{ccccccc} 1 & 0 & 0 & 0 & 1 & 1 & 1 \\ 0 & 1 & 0 & 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & 0 & 0 & 1 & 1 & 1 & 0 \\ \end{array}\right).$$ Then $(a,b,c) G = (a,b,c,d,a+c+d,a+b+c,a+b+c)$, in particular $(1,0,1,0)G =(1,0,1,0,0,1,0)$.