Consider the generator matrix for the $(7,4)$ Hamming code shown in Q$5.$

Here, the number of uncoded bits k $=4.$

$($a$)$ Find all the possible combinations of four uncoded binary bits.

$($b$)$ Use the generator matrix to encode these uncoded bits $($encode four bits at a time$).$

$[25$ pts$]($bonus$)$ Consider the generator matrix for the $(7,4)$ Hamming code shown in Q$5.$

Here, the number of uncoded bits $k=4.$

$($a$)$ Find all the possible combinations of four uncoded binary bits.

$($b$)$ Use the generator matrix to encode these uncoded bits $($encode four bits at a time$).$

You may do this manually or using a programming language. Make sure to use the modulo$-2$

operation while encoding.You may do this manually or using a programming language. Make sure to use the modulo$-2$ operation while encoding.