distance is a measure of how many bits are different, right? Yes, this is called the hamming distance. This is the code word space. We definitely want this function to be injective because given the code word you want to be able to recover the message but we want it to be beyond injective. It's a property called distance that if you take any two code words in the codeword space, so if you take Any two messages and encode them, you want the resulting code words to be far apart from one another. And then as long as there are no other code words floating around near to the code word that Bob received, then at least theoretically should be able to recovered

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