Consider a repetition code to detect $m$ errors. What is the smallest repetition parameter $k$ (i.e., the number of repetitions per bit) it should be used so that the code can always detect $m$ errors?
To be clear I know that you need $k=2m+1$ to correct errors, I am asking what is $k$ if you only want to detect errors. I know the answer is $m+1$.
I read some articles about Hamming codes but I didn't understand the explanation. I also read this post but it wasn't helpful enough: Hamming distance required for error detection and correction
Let a code make 3 repetitions and add a parity bit to the message. For example, $1010$ is encoded as $111 \; 000 \; 111 \; 000 \; 0$. How many (maximum) errors can this code identify? How many can it fix?
(The answer is fix one and identify three but I don't understand why.)