Ment
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I have only checked the consistency of the condition so far.
The idea is that the transaction has 7 bits, the message has 4 bits, and there are 8 possible locations for the error (from the first to the seventh bit, as well as the absence of an error), which is 3 bits. In total, the size of the transaction is equal to the size of the message plus the error information, so a solution should exist.