Abstract We present an explicit method for designing DNA codes from reversible self-dual codes over the finite field G F ( 4 ) of order 4. We use Euclidean reversible self-dual codes (Euclidean RSD codes for short) since they have some advantages in designing DNA codes; hence, in this work RSD codes mean Euclidean RSD codes. We first work on a construction method for reversible self-dual codes over G F ( 4 ) , and we study their properties in the aspect of their connection to DNA codes. We then obtain an efficient and feasible algorithm for designing DNA codes from RSD codes over G F ( 4 ) . We point out that our algorithm takes advantage of reversibility and self-duality of RSD codes over G F ( 4 ) . Finally, we produce DNA codes up to length 42 using our method and discuss the GC-weight distributions of DNA codes. We obtain many new DNA codes with better parameters when compared to the previously known results, and we also improve the lower bounds on the maximum size of DNA codes of a fixed code length and dimension.

中文翻译：

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基于 GF(4) 的可逆自对偶代码设计 DNA 代码

摘要 我们提出了一种在 4 阶有限域 GF ( 4 ) 上从可逆自对偶码设计 DNA 代码的显式方法。我们使用欧几里德可逆自对偶码（简称 Euclidean RSD 码），因为它们在设计上有一些优势。 DNA 代码；因此，在这项工作中，RSD 代码表示欧几里得 RSD 代码。我们首先研究了 GF ( 4 ) 上可逆自对偶代码的构造方法，并在它们与 DNA 代码的连接方面研究了它们的特性。然后，我们得到了一种高效可行的算法，用于在GF(4)上从RSD 代码设计DNA 代码。我们指出我们的算法利用了 GF(4) 上 RSD 码的可逆性和自对偶性。最后，我们使用我们的方法生成长度为 42 的 DNA 代码，并讨论 DNA 代码的 GC 权重分布。