I'm learning the coding theory and referring the textbook "Codes: An Introduction to Information Communication and Cryptography" written by Norman L. Biggs. In Section 3.7, the author proved that a Huffman code is optimal. I think (from his proof with binary case) he meant that code is optimal on the PF (prefix-free) sense. Is my thought true?
Since he defined "optimal" on UD (uniquely-decodable) codes, I want to know whether there is an optimal UD code which is not PF. I tried few examples and I failed.
Thanking you.