Motivated by DNA storage in living organisms and inspired by biological mutation processes, this study explores the reverse-complement string-duplication system. We commence our investigation by introducing an optimal $q$-ary reverse-complement-duplication code construction for duplication length $1$ and any number of duplications, achieving a size of $\Theta(q^n)$. Subsequently, we establish a fundamental limitation, proving that for duplication lengths greater than $1$, all reverse-complement-duplication codes correcting any number of duplications possess a size of $o(q^n)$. Further, we present a construction of reverse-complement-duplication codes with a duplication length of $2$, demonstrating a redundancy of at most $\log_q(n/2) + \log_q(\log_q(n)+1) + 2 + \log_q(3)$. Finally, we contribute an explicit construction for $q$-ary codes addressing a single classical tandem duplication for any $k$. The redundancy of these codes is $\log_q(n/k) + 1 + (k-1)\log_q(\log_q(2n/k)+1)$.

翻译：受生物体内DNA存储及生物突变过程的启发，本研究探索了反转互补字符串重复系统。我们首先引入一种针对重复长度1和任意重复次数的最优$q$元反转互补重复码构造，其规模达到$\Theta(q^n)$。随后建立基本限制条件，证明对于大于1的重复长度，所有能纠正任意重复次数的反转互补重复码的规模均为$o(q^n)$。进一步地，我们提出重复长度为2的反转互补重复码构造方案，其冗余至多为$\log_q(n/2) + \log_q(\log_q(n)+1) + 2 + \log_q(3)$。最后，针对任意$k$的单次经典串联重复，我们贡献了一种显式$q$元码构造方法。这类码的冗余度为$\log_q(n/k) + 1 + (k-1)\log_q(\log_q(2n/k)+1)$。