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In this paper, we construct an infinite family of binary linear codesassociated with double cosets with respect to certain maximal parabolicsubgroup of the orthogonal group O(2n+1,q). Here q is a power of two. Then weobtain an infinite family of recursive formulas generating the odd powermoments of Kloosterman sums with trace one arguments in terms of thefrequencies of weights in the codes associated with those double cosets inO(2n+1,q) and in the codes associated with similar double cosets in thesymplectic group Sp(2n,q). This is done via Pless power moment identity and byutilizing the explicit expressions of exponential sums over those double cosetsrelated to the evaluations of "Gauss sums" for the orthogonal group O(2n+1,q).

An Infinite Family of Recursive Formulas Generating Power Moments of Kloosterman Sums with Trace One Arguments: O(2n+1,2^r) Case