Vector representations and related matrices of DNA primary sequence based on L-tuple

We consider to construct 4L-components vectors for a DNA primary sequence based on the L-tuple. For two DNA sequences, using the corresponding vectors, we construct a set of L × L matrices called related matrix. The mathematical characterization from the constructed matrices have been selected to characterize the degree of similarity between the two DNA sequences. The search for similar sequences of a query sequence from a database of 39 library sequences and the construction of phylogenetic tree of H5N1 avian influenza virus illustrate the utility of the matrices for DNA sequences.