Supplement to: Code Spectrum and Reliability Function: Binary Symmetric Channel

A much simpler proof of Theorem 1 from [1] is presented below, using notation and formulas numeration of [1]. The text below replaces the subsection General case from §4 of [1, p. 11]. General case. In the general case for some ω we are interested in a pairs (xi,xj) with dij = ωn. But there may exist a pairs (xk,xl) with dkl < ωn. Using the “cleaning” procedure [2] we show that the influence of such pairs (xk,xl) on the value Pe is not large. It will allow us to reduce the general case to the model one. Note that if 1 n logXmax(t, ω) = o(1) , n → ∞ , (S.1)