DNA storage has emerged as an important area of research. The reliability of a DNA storage system depends on designing those DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy the newly introduced constraint, a generalization of the non-homopolymers constraint. In particular, each codeword of the DNA code has the specific property that any two consecutive sub-strings of the DNA codeword will not be the same. This is apart from the usual constraints such as Hamming, reverse, reverse-complement and GC-content. We believe that the new constraints proposed in this paper will provide significant achievements in reducing the errors, during reading and writing data into the synthetic DNA strings. We also present a construction (based on a variant of stochastic local search algorithm) to determine the size of the DNA codes with a constraint that each DNA codeword is free from secondary structures in addition to the usual constraint. This further improves the lower bounds from the existing literature, in some specific cases. A recursive isometric map between binary vectors and DNA strings is also proposed. By applying this map over the well known binary codes, we obtain classes of DNA codes with all of the above constraints, including the property that the constructed DNA codewords are free from the hairpin like secondary structures.

DNA储存已成为重要的研究领域。DNA存储系统的可靠性取决于设计足够不同的那些DNA字符串（称为DNA代码）。在这项工作中，我们介绍了满足新引入的约束（非均聚物约束的一般化）的DNA代码。特别地，DNA代码的每个代码字具有特定特性，即DNA代码字的任何两个连续的子串都不相同。这与常见的约束条件（例如汉明，反向，反向互补和GC）不同-内容。我们相信，本文提出的新约束将在减少将数据读取和写入合成DNA字符串的错误中取得重大成就。我们还提出了一种结构（基于随机局部搜索算法的一种变体），用于确定DNA代码的大小，并具有一个约束条件：除了通常的约束条件之外，每个DNA代码字均不含二级结构。在某些特定情况下，这进一步改善了现有文献的下限。还提出了二进制向量和DNA字符串之间的递归等距图。通过将此图应用于众所周知的二进制代码，我们获得了具有上述所有约束的DNA代码类别，包括所构造的DNA代码字没有发夹状二级结构的特性。