I want to compress a binary number (e.g $128$ bit number) to a less bit number. It number should be send and again converted to initial number ($128$ bit)
2026-03-31 23:47:40.1775000860
Reduction of binary number
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Interpolating information from comments with the question...
Since you require that all possible $128$ bit strings be encodable, you do not allow any string to become longer in encoding, and you do not allow an additional round of communication to transmit additional bits, what you want is impossible.
The only way to share the answers to $128$ independent yes/no questions with another party is to tell them all $128$ answers.