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codes with restricted overlaps: expandability, constructions, and bounds

JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2025年 1-26页

作者： Stanovnik, Lidija Univ Ljubljana Fac Comp & Informat Sci Vecna Pot 113 Ljubljana 1000 Slovenia

Consider a q-ary block code satisfying the property that no l-letters long codeword's prefix occurs as a suffix of any codeword for l inside some interval. We determine a general upper bound on the maximum size of these codes and a tighter bound for codes where overlaps with lengths not exceeding k are prohibited. We then provide constructions for codes with various restrictions on overlap lengths and use them to determine lower bounds on the maximum sizes. In particular, we construct (1,k)-overlap-free codes where k >= n/2 and n denotes the block size, expand a known construction of (k, n-1)-overlap-free codes, and combine the ideas behind both constructions to obtain (t(1),t(2))-overlap-free codes and codes that are simultaneously (1,k) and (n-k, n-1)-overlap-free for some . In the case when overlaps of lengths between 1 and k are prohibited, we complete the characterisation of non-expandable codes initiated by Cai, Wang, and Feng (IEEE Trans Inf Theory, 2023).

关键词： (1,k)-overlap-free code (t(1),t(2))-overlap-free code Non-overlapping code weakly mutually uncorrelated code

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

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COMPUTERS IN BIOLOGY AND MEDICINE 2023年第1期165卷 107439-107439页

作者： Lu, Xiaozhou Kim, Sunghwan Univ Ulsan Dept Elect Elect & Comp Engn Ulsan 44610 South Korea

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.

关键词： DNA storage Primer design weakly mutually uncorrelated code Maximum run length

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