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

https://hrcak.srce.hr/83078

Publication date:

12.6.2012.

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