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We consider a new family of codes, termed asymmetric Lee distance codes, thatarise in the design and implementation of DNA-based storage systems and systemswith parallel string transmission protocols. The codewords are defined over aquaternary alphabet, although the results carry over to other alphabet sizes;furthermore, symbol confusability is dictated by their underlying binaryrepresentation. Our contributions are two-fold. First, we demonstrate that thenew distance represents a linear combination of the Lee and Hamming distanceand derive upper bounds on the size of the codes under this metric based onlinear programming techniques. Second, we propose a number of codeconstructions which imply lower bounds.

Asymmetric Lee Distance Codes for DNA-Based Storage