2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134309A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat in a unified way both a low and a high rate cases. In particular, the earlier known upper bounds are improved, and a new derivation of the sphere-packing bound is presented.23 pages, to be published in Problems of Information TransmissionInformation Theorytext