An Infinite Family of Recursive Formulas Generating Power Moments of Kloosterman Sums with Trace One Arguments: O(2n+1,2^r) Case. (arXiv:0909.0809v1 [math.NT])

In this paper, we construct an infinite family of binary linear codes
associated with double cosets with respect to certain maximal parabolic
subgroup of the orthogonal group O(2n+1,q). Here q is a power of two. Then we
obtain an infinite family of recursive formulas generating the odd power
moments of Kloosterman sums with trace one arguments in terms of the
frequencies of weights in the codes associated with those double cosets in
O(2n+1,q) and in the codes associated with similar double cosets in the
symplectic group Sp(2n,q). 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 group O(2n+1,q).

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Original source : http://arxiv.org/abs/0909.0809...