Optimal Binary Codes for Small Rates of Transmission of Information

Let us suppose that the input alphabet of a channel consists of two symbols. We consider the optimal method of transmission of $N$ code entries through the channel where the length of transmission is for $n\to\infty$ and $N=\operatorname{const}$. Formula (21) gives an asymptotic expression for the optimal probability of error if the transition matrix of the channel is symmetrical in a certain sense.