  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.
