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In this paper, we construct four infinite families of ternary linear codesassociated with double cosets in $O(2n+1,q)$ with respect to certain maximalparabolic subgroup of the special orthogonal group $SO(2n+1,q)$. Here $q$ is apower of three. Then we obtain two infinite families of recursive formulas, theone generating the power moments of Kloosterman sums with $``$trace nonzerosquare arguments" and the other generating the even power moments of those.Both of these families are expressed in terms of the frequencies of weights inthe codes associated with those double cosets in $O(2n+1,q)$ and in the codesassociated with similar double cosets in the symplectic group $Sp(2n,q)$. Thisis done via Pless power moment identity and by utilizing the explicitexpressions of exponential sums over those double cosets related to theevaluations of $"$Gauss sums" for the orthogonal group $O(2n+1,q)$.

Infinite Families of Recursive Formulas Generating Power Moments of  Ternary Kloosterman Sums with Trace Nonzero Square Arguments: $O(2n+1,2^{r})$  Case