Hyperquadratic continued fractions over a finite field of odd   characteristic with partial quotients of degree 1
  In 1986, some examples of algebraic, and nonquadratic, power series over a finite prime field, having a continued fraction expansion with partial quotients all of degree one, were discovered by W. Mills and D. Robbins. In this note we show how these few examples are included in a very large family of continued fractions for certain algebraic power series over an arbitrary finite field of odd characteristic. 
Alain Lasjaunias and Jia-Yan Yao
math.NT