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This paper presents constructions of DNA codes that satisfy biological and combinatorial constraints for DNA-based data storage systems. We introduce an algorithm that generates DNA blocks containing sequences that meet the required constraints for DNA codes. The constructed DNA sequences satisfy biological constraints: balanced GC-content, avoidance of secondary structures, and prevention of homopolymer runs.

DNA-based data storage systems face practical challenges due to the high cost of DNA synthesis. A strategy to address the problem entails encoding data via topological modifications of the DNA sugar-phosphate backbone. The DNA Punchcards system, which introduces nicks (cuts) in the DNA backbone, encodes only one bit per nicking site, limiting density. We propose DNA Tails, a storage paradigm that encodes nonbinary symbols at nicking sites by growing enzymatically synthesized single-stranded DNA of varied lengths.