Infinite families of recursive formulas generating power moments of Kloosterman sums: O^- (2n, 2^r) case

Details Infinite families of recursive formulas generating power moments of Kloosterman sums: O^- (2n, 2^r) case Infinite families of recursive formulas generating power moments of Kloosterman sums: O^- (2n, 2^r) case

2009-01-09

arxiv.org/abs/0901.1287v1

Mathematics

Number Theory

Scientific paper

In this paper, we construct eight infinite families of binary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group $SO^-(2n,2^r)$. Then we obtain four infinite families of recursive formulas for the power moments of Kloosterman sums and four 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 $O^-(2n,2^r)$

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