  An antidictionary code is a lossless compression algorithm using an
antidictionary which is a set of minimal words that do not occur as substrings
in an input string. The code was proposed by Crochemore et al. in 2000, and its
asymptotic optimality has been proved with respect to only a specific
information source, called balanced binary source that is a binary Markov
source in which a state transition occurs with probability 1/2 or 1. In this
paper, we prove the optimality of both static and dynamic antidictionary codes
with respect to a stationary ergodic Markov source on finite alphabet such that
a state transition occurs with probability $p (0 < p \leq 1)$.
