Why it is not a Huffman code
(Minimum number of codewords) (Binary complete) Huffman code of maximal code length $n$ must have at least $n+1$ codewords.

The maximal code length of codewords $\{01, 10\}$ is 2. However, there are only two codewords. So those codewords is not a Huffman code.



(Exercise.) Prove the claim of the minimum number of codewords of Huffman code.