Predefined sets of short DNA sequences are commonly used as barcodes to identify individual biomolecules in pooled populations. Such use requires either sufficiently small DNA error rates, or else an error-correction methodology. Most existing DNA error-correcting codes (ECCs) correct only one or two errors per barcode in sets of typically ≲10 barcodes. We here consider the use of random barcodes of sufficient length that they remain accurately decodable even with ≳6 errors and even at Formula: see text or 20% nucleotide error rates. We show that length ∼34 nt is sufficient even with ≳10 barcodes. The obvious objection to this scheme is that it requires comparing every read to every possible barcode by a slow Levenshtein or Needleman-Wunsch comparison. We show that several orders of magnitude speedup can be achieved by (i) a fast triage method that compares only trimer (three consecutive nucleotide) occurence statistics, precomputed in linear time for both reads and barcodes, and (ii) the massive parallelism available on today's even commodity-grade Graphics Processing Units (GPUs). With 10 barcodes of length 34 and 10% DNA errors (substitutions and indels), we achieve in simulation 99.9% precision (decode accuracy) with 98.8% recall (read acceptance rate). Similarly high precision with somewhat smaller recall is achievable even with 20% DNA errors. The amortized computation cost on a commodity workstation with two GPUs (2022 capability and price) is estimated as between US$ 0.15 and US$ 0.60 per million decoded reads.