2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/133673A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat both low and high rate cases in a unified way. In particular, the earlier known upper bounds are improved, and a new derivation of the sphere-packing bound is presented.24 pages, 1 figureInformation Theorytext