On similarity codes

We introduce a biologically motivated measure of sequence similarity for quaternary N-sequences, extending Humming similarity. This measure is the sum over the length of the sequences of "alphabetic" similarities at all positions. Alphabetic similarities are defined, symmetrically on the Cartesian square of the alphabet. These similarities equal zero whenever the two elements differ. In distinction to Hamming similarity, however, our alphabetic similarities 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 codes and applied for DNA sequences.