Infinite Families of Recursive Formulas Generating Power Moments of Ternary Kloosterman Sums with Square Arguments Associated with $O^{-}_{}(2n,q)$

Details Infinite Families of Recursive Formulas Generating Power Moments of Ternary Kloosterman Sums with Square Arguments Associated with $O^{-}_{}(2n,q)$ Infinite Families of Recursive Formulas Generating Power Moments of Ternary Kloosterman Sums with Square Arguments Associated with $O^{-}_{}(2n,q)$

2009-09-07

arxiv.org/abs/0909.1178v1

Mathematics

Number Theory

20 pages

Scientific paper

In this paper, we construct eight infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the special orthogonal group $SO^{-}(2n,q)$. Here ${q}$ is a power of three. Then we obtain four infinite families of recursive formulas for power moments of Kloosterman sums with square arguments and four infinite families of recursive formulas for even power moments of those 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 $O^{-}(2n,q)$.

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