  In this paper, we construct two ternary linear codes $C(SO(3,q))$ and
$C(O(3,q))$, respectively associated with the orthogonal groups $SO(3,q)$ and
$O(3,q)$. Here $q$ is a power of three. Then we obtain two recursive formulas
for the power moments of Kloosterman sums with $``$trace nonzero square
arguments" in terms of the frequencies of weights in the codes. This is done
via Pless power moment identity and by utilizing the explicit expressions of
Gauss sums for the orthogonal groups.
