Q$5.$ Prepare a $(n,k)$ Hamming Code such that the resulting codeword should be exactly $3$

bits long. To solve this question; you can consider any $k-$bit source code of your choice

that satisfies the Hamming Code condition. Now induce an error in the $2^{nd}$ and $3^{rd}$ bit

positions of the codeword. Perform Hamming Code operation at the receiver and prove

that Hamming Codes cannot correct multiple errors.

$(10$M$)$