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In reversible data hiding (RDH), the original cover can be losslessly restored after the embedded information is extracted. Kalker and Willems established a rate-distortion model for RDH, in which they proved out the rate-distortion bound and proposed a recursive code construction. In our previous paper, we improved the recursive construction to approach the rate-distortion bound. In this paper, we generalize the method in our previous paper using a decompression algorithm as the coding scheme for embedding data and prove that the generalized codes can reach the rate-distortion bound as long as the compression algorithm reaches entropy. By the proposed binary codes, we improve three RDH schemes that use binary feature sequence as covers, i.e., an RS scheme for spatial images, one scheme for JPEG images, and a pattern substitution scheme for binary images. The experimental results show that the novel codes can significantly reduce the embedding distortion. Furthermore, by modifying the histogram shift (HS) manner, we also apply this coding method to one scheme that uses HS, showing that the proposed codes can be also exploited to improve integer-operation-based schemes.