Consider a $(n,k)$ block code shown below and the $(3,1)$

repetition code.

Where $D$# is the message bit and $P$# is the parity bit.

Assume that the parity bits are computed by choosing P$1$

through P$3$ so that the corresponding row has even parity. The

codeword is arranged as D$1$ D$2$ D$3$ P$1$ P$2$ P$3$

It turns out that the minimum hamming distance for this code

is $d=3.$

A$.[2]$ What are the values of $n$ and $k$ for the $(n,k)$ block

code?

B$.[1]$ How many valid codewords are there in the $(n,k)$ block

code?

C$.[2]$ What is the code rate of the $(n,k)$ block code?

D$.[3]$ For a fixed gross bit rate, which code has a higher

net bit rate, the $(n,k)$ block code as described above or

the $(3,1)$ repetition code? Justify your answer by showing

your calculations.

E$.[10]$ The bits received are: $011110110101.$ Assume that all

the errors can be corrected.

using the above $(n,k)$ block code, what will be the

decoded message bits after error correction?

$2.$ using the $(3,1)$ repetition code, what will be the

decoded message bits after error correction?