We generalize the Zhang, Zhang, and Wang (ZZW) construction to produce larger code families for steganography from existing codes, which can cover the range of relative payloads more densely. We also prove that the expanded code family keeps the similar asymptotic property as the code family produced by the ZZW construction, that is, the codes follow the theoretic upper bound on embedding efficiency as relative payload tends to zero.
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Zhang et al. (2009) studied this question.