We have developed a simple and efficient algorithm to identify each member of a large collection of DNA-linked objects through the use of hybridization, and have applied it to the manufacture of randomly assembled arrays of beads in wells. Once the algorithm has been used to determine the identity of each bead, the microarray can be used in a wide variety of applications, including single nucleotide polymorphism genotyping and gene expression profiling. The algorithm requires only a few labels and several sequential hybridizations to identify thousands of different DNA sequences with great accuracy. We have decoded tens of thousands of arrays, each with 1520 sequences represented at approximately 30-fold redundancy by up to approximately 50,000 beads, with a median error rate of <1 x 10(-4) per bead. The approach makes use of error checking codes and provides, for the first time, a direct functional quality control of every element of each array that is manufactured. The algorithm can be applied to any spatially fixed collection of objects or molecules that are associated with specific DNA sequences.