Solving the error correcting code is an important goal with regard to communication theory. To reveal the error correcting code characteristics, several researchers have applied a statistical-mechanical approach to this problem. In our research, we have treated the error correcting code as a Bayes inference framework. Carrying out the inference in practice, we have applied the NMF (naive mean field) approximation to the MPM (maximizer of the posterior marginals) inference, which is a kind of Bayes inference. In the field of artificial neural networks, this approximation is used to reduce computational cost through the substitution of stochastic binary units with the deterministic continuous value units. However, few reports have quantitatively described the performance of this approximation. Therefore, we have analyzed the approximation performance from a theoretical viewpoint, and have compared our results with the computer simulation.