  In this paper, we construct four infinite families of binary linear codes
associated with double cosets with respect to certain maximal parabolic
subgroup of the orthogonal group O^+(2n,2^r). Here q is a power of two. Then we
obtain two infinite families of recursive formulas for the power moments of
Kloosterman sums and those of 2-dimensional Kloosterman sums 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 exponential sums over
those double cosets related to the evaluations of "Gauss sums" for the
orthogonal groups O^+(2n,2^r).
