Strategy for data transmission over binary channels with noiseless feedback and upper bound on the number of questions in searching with lies

A transmission strategy that allows the sender to deliver any of M messages to the receiver over a binary channel when at most e errors can occur is presented. The total number of bits required by the strategy differs from the known lower bound by 3e. This statement simultaneously gives a new upper bound on the number of questions in the process of searching with lies known as the "Ulam's game".