We introduce a new family of codes, termed asymmetric Lee distance (ALD) codes, designed to correct errors arising in DNA-based storage systems and systems with parallel string transmission protocols. ALD codes are defined over a quaternary alphabet and analyzed in this particular setting, but the derived results hold for other alphabet sizes as well. Our technical contributions are twofold. First, we derive upper bounds on the size of the codes under the ALD metric based on linear programming techniques. Second, we propose a number of code constructions, which imply lower bounds.
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Gabrys et al. (2017) studied this question.
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