Systems and techniques for extracting information-containing payloads from DNA or other polynucleotides are provided. Decoding the sequence of payload regions from multiple polynucleotides to obtain encoded information includes sequencing the molecules with a polynucleotide sequencer. Reads generated by the polynucleotide sequencer can include information from multiple different sources mixed together. Primer sequences present in the reads identify which reads contain information from the same source. A computationally efficient technique for finding primer sequences in the reads includes comparing hashes of the reads and hashes of primer sequences to find an approximate location then computing edit distances between the primer sequences and the reads to find an exact location. Reads that include the same primer sequences may be clustered together. Sequences of the payload regions are extracted based on the locations of the primer sequences.