Construction of DNA codes with multiple constrained properties

Abstract

DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization of its nucleotides. The formation of large stem-length secondary structures makes the sequences chemically inactive towards synthesis and sequencing processes. Furthermore, in DNA computing, other constraints like homopolymer run length also introduce complications. In this paper, our goal is to tackle the problems due to the creation of secondary structures in DNA sequences along with constraints such as not having a large homopolymer run length. This paper presents families of DNA codes with secondary structures of stem length at most two and homopolymer run length at most four. We identified \(\mathbb {Z}_{11}\) as an ideal structure to construct DNA codes to avoid the above problems. By mapping the error-correcting codes over \(\mathbb {Z}_{11}\) to DNA nucleotides, we obtained DNA codes with rates 0.5765 times the corresponding code rate over \(\mathbb {Z}_{11}\), including some new secondary structure-free and better-performing codes for DNA-based data storage and DNA computing purposes.