On Secondary Structure Avoiding DNA codes with Reversible and Reversible-Complement Constraints

For various applications of DNA computing like DNA-based data storage, DNA codes are studied with properties such as avoiding secondary structures and satisfying Reversible and Reversible-Complement constraints. A chemically active single-strand DNA folds upon itself and forms structures called secondary structures. In this work, motivated by the Reed-Muller code, families of DNA codes are designed that avoid secondary structures and satisfy Reversible and Reversible-Complement constraints. In addition, for some families, the concatenations of any DNA codewords also avoid secondary structures. Also, for a specific case, code rates for the DNA codes of the families are non-vanishing for large lengths.