2024/09/10 by Guodong Wang, Hongwei Liu, Wang, Guodong +3
Biochemistry, Genetics and Molecular Biology · Computer Science · #94B15 #94B60 #Advanced biosensing and bioanalysis techniques #Algorithms and Data Compression #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2409.06519
openalex publication_date 2024/09/10 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28
DNA codes have garnered significant interest due to their utilization in digital media storage, cryptography, and DNA computing. In this paper, we first extend the results of constructing reversible group codes \citeCengellenmis and reversible composite group codes \citeKorban5 to general even-order finite groups. By using these results, we give parallel searching algorithms to find some new DNA codes with better parameters. Secondly, by mapping codes over \mathbbF4 to DNA codes, we establish a relationship between the GC-weight enumerator of DNA codes and the Hamming weight enumerator of their trace codes, which greatly improves the computational efficiency of searching for DNA codes. Based on this relationship, we propose an efficient algorithm for generating DNA codes with 50% GC-content. Furthermore, we find that there is no direct connection between the GC-weight enumerator of a DNA code and the GC-weight enumerator of its dual code. Finally, we present algorithms for determining whether a DNA code is free from secondary structures or conflict-free, and some new DNA codes with better parameters under multiple constraints are obtained, which are listed in Tables 1 and 4.