2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134352We give a new and short proof of the Mallows-Sloane upper bound for self-dual codes. We formulate a version of Greene's theorem for normalized weight enumerators. We relate normalized rank-generating polynomials to two-variable zeta functions. And we show that a self-dual code has the Clifford property, but that the same property does not hold in general for formally self-dual codes.12 pagesCombinatoricsInformation TheoryNumber Theory05B35; 14G15; 94B65text