  There is a theory of continued fractions for Laurent series in x^{-1} with
coefficients in a field F. This theory bears a close analogy with classical
continued fractions for real numbers with Laurent series playing the role of
real numbers and the sum of the terms of non-negative degree in x playing the
role of the integral part.
  In this paper we survey the Laurent series u, with coefficients in a finite
extension of gf(2), that satisfy an irreducible equation of the form
  a_0(x)+ a_1(x)u+a_2(x)u^2 + a_3(x)u^3=0
  with a_3 \ne 0 and where the a_i are polynomials of low degree in x with
coefficients in gf(2). We are particularly interested in the cases in which the
sequence of partial quotients is bounded (only finitely many distinct partial
quotients occur). We find that there are three essentially different cases when
the a_i(x) have degree \le 1. We also make some empirical observations
concerning relations between different Laurent series roots of the same cubic.
