Quartic Power Series in f₃((t⁻¹))

We are concerned with power series in 1/T over a finite field of 3 elements $\F_3$. In a previous article, Alain Lasjaunias investigated the existence of particular power series of elements algebraic over $\F_3[T]$, having all partial quotients of degree 1 in their continued fraction expansion. Here, we generalize his result and we make a conjecture about the elements with all partial quotients of degree 1, except maybe the first ones.