Motivated by studies of data retrieval in polymer-based storage systems, we consider the problem of reconstructing a multiset of binary strings that have the same length and the same weight from the compositions of their prefixes and suffixes of every possible length. We provide necessary and sufficient conditions for which unique reconstruction up to reversal of the strings is possible. Additionally, we present two algorithms for reconstructing strings from the compositions of prefixes and suffixes of constant-length constant-weight strings.

翻译：受基于聚合物的存储系统中数据检索研究的启发，我们研究了从所有可能长度的前缀和后缀组合中重构具有相同长度和相同权重的二进制字符串多重集的问题。我们给出了字符串在反转意义下可唯一重构的充分必要条件。此外，我们提出了两种从恒定长度恒定权重字符串的前缀与后缀组合中重构字符串的算法。