Original scientific paper
Ternary codes associated with $O(3,3^r)$ and power moments of Kloosterman sums with trace nonzero square arguments
Dae San Kim
; Department of Mathematics, Sogang University, Seoul, Korea
Abstract
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.
Keywords
power moment; Kloosterman sum; trace nonzero square argument; orthogonal group; Pless power moment identity; weight distribution; Gauss sum
Hrčak ID:
83078
URI
Publication date:
12.6.2012.
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