  This paper studies maximum likelihood(ML) decoding in error-correcting codes
as rational maps and proposes an approximate ML decoding rule by using a Taylor
expansion. The point for the Taylor expansion, which will be denoted by $p$ in
the paper, is properly chosen by considering some dynamical system properties.
We have two results about this approximate ML decoding. The first result proves
that the order of the first nonlinear terms in the Taylor expansion is
determined by the minimum distance of its dual code. As the second result, we
give numerical results on bit error probabilities for the approximate ML
decoding. These numerical results show better performance than that of BCH
codes, and indicate that this proposed method approximates the original ML
decoding very well.
