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Hashing has been widely applied in large-scale multimodal retrieval by mapping heterogeneous modalities data into binary codes. However, most cross-modal hashing methods cannot make the most of semantic information to construct the association relations of sample pairs, resulting in unsatisfactory retrieval accuracy. Concept lattice is a powerful tool for data mining and information retrieval, and for all we know, this is the first time to combine formal concept analysis and hash learning to improve cross-modal hashing retrieval performance. In this paper, we propose a novel framework for Asymmetric Cross-modal Hashing based on Formal Concept Analysis, denoted as ACHFCA. Initially, a flash-projection three-layer semantic enhancement descriptor is designed to extract latent representations from heterogeneous modalities. Subsequently, an asymmetric hash learning framework is established to enhance the semantics of different layers based on the fine-grained similarity values reconstructed from concept lattice to reinforce the discriminative competence of the model. Finally, an effective discrete optimization algorithm is proposed, which can directly learn compact hash codes. Comprehensive experiments on MIRFlickr, NUS-WIDE and IAPR-TC12 datasets demonstrate the superior performance of ACHFCA to state-of-the-art hashing approaches.