In an error-correction code, an important constraint that the coding scheme must satisfy is that the number of added check bits should be sufficient to identify unique error patterns (note that no error is also a valid error pattern). Now suppose that we decide to use a (n, 20, 3) error correction code to transmit 20-bit messages. Whats the minimum value of n that will allow the code to correct single bit errors? Show the reason and the calculation for full credits.