2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59627We show that every p-fold strictly-cyclic branched covering of a b-bridge link in $S^3$ admits a p-symmetric Heegaard splitting - in the sense of Birman and Hilden - of genus $g=(b-1)(p-1)$. This gives a complete converse of one of the results of the two authors. Moreover, we introduce the concept of weakly p-symmetric Heegaard splittings and prove similar results in this more general context.11 pages, 2 figures, to appear in the Journal of Knot Theory and its RamificationsGeometric Topology57M12, 57R65; 20F05, 57M05, 57M25text