Lectures on DNA Codes

For q-ary n-sequences, we develop the concept of similarity functions that can be used (for q = 4) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence between two q-ary n-sequences. Codes based on similarity functions are called DNA codes [1, 2, 3]. DNA codes are important components in biomolecular computing [4] and other biotechnical applications that employ DNA hybridization assays. The main aim of the given lecture notes – to discuss lower bounds on the rate of optimal DNA codes for a biologically motivated [2] similarity function called a block similarity and for the conventional deletion similarity function [5, 6, 7] used in the theory of error-correcting codes. We also present constructions of suboptimal DNA codes based on the parity-check code detecting one error in the Hamming metric [8].