How does neural activity generate perception? Finding the combinations of spatial or temporal activity features (such as neuron identity or latency) that are consequential for perception remains challenging. We trained mice to recognize synthetic odors constructed from parametrically defined patterns of optogenetic activation, then measured perceptual changes during extensive and controlled perturbations across spatiotemporal dimensions. We modeled recognition as the matching of patterns to learned templates. The templates that best predicted recognition were sequences of spatially identified units, ordered by latencies relative to each other (with minimal effects of sniff). Within templates, individual units contributed additively, with larger contributions from earlier-activated units. Our synthetic approach reveals the fundamental logic of the olfactory code and provides a general framework for testing links between sensory activity and perception.