On similarity codes

We introduce a biologically motivated measure of sequence similarity for qu aternary N-sequences, extending Humming similarity. This measure is the sum over the length of the sequences of "alphabetic" similarities at all posit ions. Alphabetic similarities are defined, symmetrically on the Cartesian s quare of the alphabet. These similarities equal zero whenever the two eleme nts differ. In distinction to Hamming similarity, however, our alphabetic s imilarities Lake individual values whenever the two elements are identical. In this correspondence,ve derive lower and upper bounds on the rate of the corresponding quaternary nonlinear and linear codes called similarity code s and applied for DNA sequences.