Partial words for DNA coding

Abstract

A very basic problem in all DNA computations is finding a good encoding. Apart from the fact that they must provide a solution, the strands involved should not exhibit any undesired behaviour, especially they should not form secondary structures. Various combinatorial properties like repetition-freeness and involution-freeness have been proposed to exclude such misbehaviour. Another option, which has been considered, is requiring a big Hamming distance between the codewords. We propose to consider partial words for the solution of the coding problem. They, in some sense, already include the Hamming distance in the definition of compatibility and are investigated for many combinatorial properties. Thus, they can be used to guarantee a desired distance and simultaneously other properties. As the investigations on partial words are attracting more and more attention, they might be able to provide an ever-growing toolbox for finding good DNA encodings. © Springer-Verlag Berlin Heidelberg 2005.