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We formulate a framework for applying error-correcting codes (ECCs) on multilabel classification problems. The framework treats some base learners as noisy channels and uses ECC to correct the prediction errors made by the learners. The framework immediately leads to a novel ECC-based explanation of the popular random k-label sets (RAKEL) algorithm using a simple repetition ECC. With the framework, we empirically compare a broad spectrum of off-the-shelf ECC designs for multilabel classification. The results not only demonstrate that RAKEL can be improved by applying some stronger ECC, but also show that the traditional binary relevance approach can be enhanced by learning more parity-checking labels. Our research on different ECCs also helps to understand the tradeoff between the strength of ECC and the hardness of the base learning tasks. Furthermore, we extend our research to ECC with either hard (binary) or soft (real-valued) bits by designing a novel decoder. We demonstrate that the decoder improves the performance of our framework.