So I'm looking into Huffman coding, and it's a pretty simple algorithm to understand, except I was curious about one thing. Given that "a Huffman tree that omits unused symbols produces the most optimal code lengths", I was curious whether the frequency table of a Huffman tree counts towards the total length of the encoded message? I suppose this question in itself boils down to how the frequency table is stored. Is it part of the encoded message, or is it saved as a separate file?
Yes, unless the two sides agree on a pre-determined code book, the frequency table (or equivalent information sufficient to construct the decoding tree on the receiving end) must be included in the message.
Google Canonical Huffman code for a clever way to cut down on the size of this information.