Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups

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May 2009, 3(2): 167-178. doi: 10.3934/amc.2009.3.167

Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups

1.	Department of Mathematics, Sogang University, Seoul 121-742, South Korea

Received December 2008 Revised April 2009 Published May 2009

Abstract
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In this paper, we construct two infinite families of ternary linear codes associated with double cosets with respect to certain maximal parabolic subgroups of the symplectic group $S_p(2n, q)$. Here $q$ is a power of three. Then we obtain infinite families of recursive formulas for the power moments of Kloosterman sums with square arguments and for the even power moments of those in terms of the frequencies of weights in the codes. This is done via Pless power moment identities and by utilizing the explicit expressions of exponential sums over those double cosets related to the evaluations of ''Gauss sums'' for the symplectic groups $S_p(2n, q)$.

Keywords: Pless power moment identity, Kloosterman sum, weight distribution., square argument, Ternary linear code, Gauss sum, power moment, symplectic group.

Mathematics Subject Classification: 11T23, 20G40, 94B0.

Citation: Dae San Kim. Infinite families of recursive formulas generating power moments of ternary Kloosterman sums with square arguments arising from symplectic groups. Advances in Mathematics of Communications, 2009, 3 (2) : 167-178. doi: 10.3934/amc.2009.3.167

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