Lectures on DNA Codes

Abstract: 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. DNA codes are important components in biomolecular computing 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 similarity function called a block similarity and for the conventional deletion similarity function 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.