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This paper presents Reed-Solomon coded single-stranded representation learning (RSRL), a novel end-to-end model for learning representations for lossless DNA data storage. In contrast to existing learning-based methods, RSRL is inspired by both error-correction codec and structural biology. Specifically, RSRL first learns the representations for the subsequent storage from the binary data transformed by the Reed-Solomon codec (RS code). Then, the representations are masked by an RS-code-informed mask to focus on correcting the burst errors occurring in the learning process. The synergy of RS masks and graph attention enables active error localization, breaking through the limitations of traditional passive error correction. With the decoded representations with error corrections, a novel biologically stabilized loss is formulated to regularize the data representations to possess stable single-stranded structures. By incorporating these novel strategies, RSRL can learn highly durable, dense, and lossless representations for subsequent storage tasks in DNA sequences. The proposed RSRL has been compared with a number of baselines in real-world tasks of multi-type data storage. The experimental results obtained demonstrate that RSRL can store diverse types of data with much higher information density and durability, but much lower error rates.