We present a novel method for the encoding and decoding of multiplexed biochemical assays. The method enables a theoretically unlimited number of independent targets to be detected and uniquely identified in any combination in the same sample. For example, the method offers easy access to 12-plex and larger PCR assays, as contrasted to the current 4-plex assays. This advancement would allow for large panels of tests to be run simultaneously in the same sample, saving reagents, time, consumables, and manual labor, while also avoiding the traditional loss of sensitivity due to sample aliquoting. Thus, the presented method is a major technological breakthrough with far-reaching impact on biotechnology, biomedical science, and clinical diagnostics. Herein, we present the mathematical theory behind the method as well as its experimental proof of principle using Taqman PCR on sequences specific to infectious diseases.