Continued Fractions for Algebraic Formal Power Series over a Finite Base Field

We consider the continued fraction expansion of certain algebraic formal power series when the base field is finite. We are concerned with the property of the sequence of partial quotients being bounded or unbounded. We formalize the approach introduced by Baum and Sweet (1976), which applies to the elements of a particular subset of algebraic power series. We illustrate this method with a result when the base field is 2.