b$)$

A different non$-$standard Hamming $(7,4)$ code is used to encode a message that is received as

$(1,0,1,0,1,1,0).$

If this message indicates there is an error in the $3$rd digit, which Hamming matrix below was used?

$([1,1,0,0,1,1,0$

$0,1,1,1,1,0,0$

$0,0,0,1,1,1,1]),([1,1,0,1,0,1,0$

$0,0,1,1,0,1,1$

$1,0,0,0,1,1,1]),([0,1,0,0,1,1,1$

$1,1,1,0,0,1,0$

$1,1,0,1,1,0,0])$

$([1,0,1,0,1,1,0$

$0,0,1,1,1,0,1$

$0,1,0,0,1,1,1]),([1,1,1,0,0,1,0$

$1,1,0,1,0,0,1$

$0,1,0,0,1,1,1]),([1,0,0,0,1,1,1$

$0,1,0,1,1,1,0$

$1,0,1,1,0,1,0])$