We find a method for constructing DNA codes with single-deletion-correcting capability. We first present an explicit algorithm for the construction of the q-ary single-deletion-correcting codes (abbreviated as SDC codes) using a class of the complementary information set codes (abbreviated as CIS codes), where q is a power of a prime. We then show that the encoding/decoding scheme of the CIS codes with single-deletion-correcting capability has a simple deterministic algorithm. Finally, applying our algorithm to the generated DNA codes with appropriate modification, we obtain the DNA codes with single-deletion-correcting capability. We present some various examples of such DNA codes, and we also obtain some lower bounds on the maximum size of the single-deletion-correcting DNA codes.

中文翻译：

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使用CIS编码构建单删改DNA编码

我们找到了一种构建具有单删除纠正能力的 DNA 代码的方法。我们首先提出了一种使用一类互补信息集代码（缩写为 CIS 代码）构建 q 元单删除校正代码（缩写为 SDC 代码）的显式算法，其中 q 是素数的幂. 然后我们展示了具有单删除纠正能力的 CIS 代码的编码/解码方案具有简单的确定性算法。最后，将我们的算法应用于生成的 DNA 代码，并进行适当的修改，我们得到具有单删除纠正能力的 DNA 代码。我们展示了一些此类 DNA 代码的各种示例，并且我们还获得了单删除校正 DNA 代码的最大大小的一些下限。