A fast iterative algorithm to obtain topological atomic and molecular descriptors, called Qcodes, is presented in this work. Its linear time dependence with the size of the structures and low memory requirement allows practical use for small molecules as well as macromolecular systems. The descriptors are unique and are able to sense small topological changes in atom's neighborhood. These properties make them suitable as atom and molecular identifiers to be used in database searching, force field atom typing, isomorphism, and automorphism algorithms. Examples of descriptors, their convergence behavior, sensitivity, ambiguity, and algorithm's performance are shown in this paper.