The synthesis of DNA strands remains the most costly part of the DNA storage system. Thus, to make DNA storage system more practical, the time and materials used in the synthesis process have to be optimized. We consider the most common type of synthesis process where multiple DNA strands are synthesized in parallel from a common alternating supersequence, one nucleotide at a time. The synthesis time or the number of synthesis cycles is then determined by the length of this common supersequence. In this model, we design quaternary codes that minimizes synthesis time that can correct deletions or insertions, which are the most prevalent types of error in array-based synthesis. We also propose polynomial-time algorithms that encode binary strings into these codes and show that the rate is close to capacity.

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