On probabilistic aspects of error correction codes when the number of errors is a random set

In the paper, $n$ messages each containing $N$ blocks are considered. Each block is encoded with some antinoise coding method, which can correct not more than $q$ mistakes. Here, it is assumed that the number of mistakes lies in some random subset $N_i(\omega_1)$, $\omega_1\in\Omega_1$ of integer numbers. The probability ${\mathbf P}(A)$ of the event $A$ is studied which means that all the mistakes would be corrected. Probability ${\mathbf P}(A)$ is formulated in terms of conditional probabilities. It is shown that as $n, N\to\infty$ so that $\alpha=n/N\to\alpha_0<\infty$, at $q=1$, probabilities ${\mathbf P}(A)$ converge at almost all $\omega_1\in\Omega_1$. The limit is obtained.