Asymmetric Lee distance codes for DNA-based storage

We consider a new family of asymmetric Lee codes that arise in the design and implementation of DNA-based storage systems and systems with parallel string transmission protocols. The codewords are defined over a quaternary alphabet, although the results carry over to other alphabet sizes, and have symbol distances dictated by their underlying binary representation. Our contributions are two-fold. First, we derive upper bounds on the size of the codes under the asymmetric Lee distance measure based on linear programming techniques. Second, we propose code constructions which imply lower bounds.