We have 2 stations that communicate with each other, but we need to detect (or even correct) when something is wrong.
We use 8 binary words: each consisting of 3 bits and to send it we code it as where is the complement of and is the even parity check bit of .
We need to find the capabilities of this code (up to how many can we detect and how many can we correct). BUT, a proof is required.
This is how far I've reached so far:
First we find the hamming distance: If changes then changes, also changes. So we have a hamming distance of 3.
This means that we can detect two bit errors or correct a single error.
Can you help me write the proof for that?
(also the tags may need some refinement - comments about the downvote are welcome)