2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133400A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new region of code rates in which the random coding exponent is asymptotically tight, giving a new region in which the reliability of the BSC is known exactly. The present paper explains the relation of these results to the union bound on the error probability.10 pages, 3 figures. Presented at the 42nd Annual Allerton Conference on Communication, Control and Computing (Sept. 29 - Oct. 1, 2004). The paper will appear in the conference proceedings. Version 2 differs slightly from the published version and is the latest version of this paperInformation Theorytext