Ternary Codes Associated with $O(3,3^r)$ and Power Moments of Kloosterman Sums with Trace Nonzero Square Arguments

Details Ternary Codes Associated with $O(3,3^r)$ and Power Moments of Kloosterman Sums with Trace Nonzero Square Arguments Ternary Codes Associated with $O(3,3^r)$ and Power Moments of Kloosterman Sums with Trace Nonzero Square Arguments

2009-09-07

arxiv.org/abs/0909.1156v1

Mathematics

Number Theory

15 pages

Scientific paper

In this paper, we construct two ternary linear codes $C(SO(3,q))$ and $C(O(3,q))$, respectively associated with the orthogonal groups $SO(3,q)$ and $O(3,q)$. Here $q$ is a power of three. Then we obtain two recursive formulas for the power moments of Kloosterman sums with $``$trace nonzero square arguments" 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 Gauss sums for the orthogonal groups.

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