From https://en.wikipedia.org/wiki/Locally_testable_code https://en.wikipedia.org/wiki/Locally_testable_code : "Clearly, any valid codeword should be accepted

From https://en.wikipedia.org/wiki/Locally_testable_code https://en.wikipedia.org/wiki/Locally_testable_code : "Clearly, any valid codeword should be accepted as a codeword, but strings that are not codewords could be only one bit off, which would require many (certainly more than a constant number) probes. To account for this, testing failure is only defined if the string is off by at least a set fraction of its bits. This implies words of the code must be longer than the input strings by adding some redundancy."