Q$4.$ Channel Coding

a$)$ Consider the following block code $C=\{0000,0011,1100,0110\}$ to be used for channel coding.

Is this code linear? What is the minimum distance $d$ of the code? How many errors can it

detect? How many errors can it correct?

b$)$ Consider the following block code $C=\{0000,1111,0011,1100\}.$ Is this code linear? What is

the minimum distance $d$ of the code? How many errors can it detect? How many errors can it

correct?

c$)$ Construct an extended block code by adding one coded bit to the block code in b$)$ such that

the extended code can correct one error.

d$)$ Consider a binary $(n,M,d)$ block code with $n=3$ and $M=8.$ Show that $d$ is upper bounded

by $1.$

e$)$ Consider a binary $(n,M,d)$ block code with $n=5$ and $M=8.$ Show that $d$ is upper bounded

by $3.$