# INFINITE FAMILIES OF RECURSIVE FORMULAS GENERATING POWER MOMENTS OF TERNARY KLOOSTERMAN SUMS WITH SQUARE ARGUMENTS ASSOCIATED WITH O-(2n, q)

• Kim, Dae-San
• Published : 2011.03.01
• 38 6

#### Abstract

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).

#### Keywords

index terms-Kloosterman sum;orthogonal group;special orthogonal group;double cosets;maximal parabolic subgroup;Pless power moment identity;weight distribution

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#### Acknowledgement

Supported by : National Foundation of Kor