New Results on D

For -ary -sequences, we develop the concept of similarity functions that can be used (for ) to model a thermodynamic similarity on DNA sequences. A similarity function is identified by the length of a longest common subsequence between two -ary -sequences. Codes based on similarity functions are called DNA codes [10]. DNA codes are important components in biomolecular computing and other biotechnical applications that employ DNA hybridization assays. We present our unpublished results [8] connected with the conventional deletion similarity function [1] used in the theory of error-correcting codes. The main aim of this paper – to obtain lower bounds on the rate of optimal DNA codes for a biologically motivated [11], [12], [13] similarity function called a similarity of blocks. We also present constructions of suboptimal DNA codes based on the parity-check code detecting one error in the Hamming metric [3].