Efficient DNA Synthesis Codes with Error Correction and Runlength Limited Constraint

DNA synthesis remains the most costly part of the DNA data storage. In this work, we consider a popular synthesis method that generates multiple DNA strands in parallel from a fixed supersequence
$S$
, one nucleotide at a time. Under this assumption, the synthesis time (or the number of synthesis cycles) is then determined by the length of the common supersequence. In this work, we propose constructions of quaternary codes that simultaneously (i) restrict the maximum synthesis time, (ii) correct a single deletion or insertion error, and (iii) satisfy the runlength limited constraint, a crucial biochemical constraint in a DNA storage channel. For certain parameters, we provide an improved construction of DNA codes with a smaller synthesis time while costing less redundancy as compared to the best-known result in the literature.