On DNA Codes With Multiple Constraints

We consider the problem of designing a set of DNA sequences (DNA codes) for various DNA computing applications, such as DNA based data storage. A chemically active DNA sequence forms unlikely secondary structure by folding back onto itself by hybridization among base pairs. DNA sequences with secondary structures are less active chemically and are needed to unfold before reading. On the other side, during synthesis and sequencing of DNA sequences with homopolymers of large run-length, errors occur frequently. In this letter, we have presented families of DNA codes with several properties such as DNA sequences free from secondary structures of stem length more than two and also free from homopolymers of run-length more than four. All constructed DNA sequences of any DNA codes are sufficiently dissimilar to their reverse-complement DNA sequences. Further, DNA sequences obtained by concatenating all those DNA sequences also avoid secondary structures and homopolymers.