Weakly mutually uncorrelated codes with maximum run length constraint for DNA storage

Abstract

DNA storage systems have begun to attract considerable attention as next-generation storage technologies due to their high densities and longevity. However, efficient primer design for random-access in synthesized DNA strands is still an issue that needs to be solved. Although previous studies have explored various constraints for primer design in DNA storage systems, there is no attention paid to the combination of weakly mutually uncorrelated codes with the maximum run length constraint. In this paper, we first propose a code design by combining weakly mutually uncorrelated codes with the maximum run length constraint. Moreover, we also explore the weakly mutually uncorrelated codes to satisfy combinations of maximum run length constraint with more constraints such as being almost-balanced and having large Hamming distance, which are also efficient constraints for random-access in DNA storage systems. To guarantee that the proposed codes can be adapted to primer design with variable length, we present modified code construction methods to achieve different lengths of the code. Then, we provide an analysis of the size of the proposed codes, which indicates the capacity to support primer design. Finally, we compare the codes with those of previous works to show that the proposed codes can always guarantee the maximum run length constraint, which is helpful for random-access for DNA storage.