Let $C \in \{ 0,1\}^7 $ be a code with the following code words :
0000000, 1110000, 0001111, 1001001, 0110110, 1000110, 0111001, 0010101, 1101010, 0011010, 1100101, 0100011, 1011100, 0101100, 1010011, 1111111.
Determine the code rate of this code.
So the formula is $R = \frac{log_q |C|}{n}$ where $q$ is the number of Symbols in the alphabet and $n$ is the block length.
In this particular case my assumption is that $q=128$ and $n=7$ and $|C|=16$. With this assumption I get that the Code rate is $R=\frac{4}{49}$. I am doubtful because this seems to be a pretty bad code rate. Can anyone please confirm that this is the correct code rate.
Your code rate is $4/7$. Just forget about the formulas and understand the essence of coding. So the question is how many information bits do you have and how many coding bits? Code bits $=7$ this is what we already know. You are given $16$ code words and from this you need to find how many information bits you have. How many? and why?