  In steganography, we always hope to maximize the embedding payload subject to
an upper-bounded distortion. We need suitable distortion measurement to
evaluate the embedding impact. However, different distortion functions exposes
different levels of distortion evaluation, implying that we have different
optimization distributions by applying different distortion functions. In
applications, the embedding distortion is caused by a certain number of
embedding operations. Instead of a predefined distortion, we actually utilize a
number of modifications to embed as many message bits as possible as long as
the modifications are acceptable. This paper focuses on the design of optimal
binary codewords for data embedding with a limited number of modification
candidates. We have proved the optimality of the designed codewords, and
proposed the way to construct the optimal binary codewords. It is pointed out
that the optimal binary code is not unique, and an optimal code can be computed
within a low computational cost.
