DNA is a promising storage medium, but its stability and occurrence of Indel errors pose a significant challenge. The relative occurrence of Guanine(G) and Cytosine(C) in DNA is crucial for its longevity, and reverse complementary base pairs should be avoided to prevent the formation of a secondary structure in DNA strands. We overcome these challenges by selecting appropriate group homomorphisms. For storing and retrieving information in DNA strings we use kernel code and the Varshamov-Tenengolts algorithm. The Varshamov-Tenengolts algorithm corrects single indel errors. Additionally, we construct codes of any desired length (n) while calculating its reverse complement distance based on the value of n.

翻译：DNA是一种有前景的存储介质，但其稳定性及插入/缺失（Indel）错误的发生构成了重大挑战。鸟嘌呤（G）与胞嘧啶（C）在DNA中的相对含量对其长期稳定性至关重要，同时应避免反向互补碱基对的形成，以防止DNA链中产生二级结构。我们通过选择合适的群同态来克服这些挑战。为在DNA链中存储和检索信息，我们采用核编码（kernel code）与Varshamov-Tenengolts算法。Varshamov-Tenengolts算法可纠正单次插入/缺失错误。此外，我们构建了任意期望长度（n）的编码，并根据n值计算其反向互补距离。