Ternary Codes Associated with O^-(2n,q) and Power Moments of Kloosterman Sums with Square Arguments

Details Ternary Codes Associated with O^-(2n,q) and Power Moments of Kloosterman Sums with Square Arguments Ternary Codes Associated with O^-(2n,q) and Power Moments of Kloosterman Sums with Square Arguments

2009-09-04

arxiv.org/abs/0909.0811v1

Mathematics

Number Theory

16 pages

Scientific paper

In this paper, we construct three ternary linear codes associated with the orthogonal group O^-(2,q) and the special orthogonal groups SO^-(2,q) and SO^-(4,q). Here q is a power of three. Then we obtain 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 identity and by utilizing the explicit expressions of "Gauss sums" for the orthogonal and special orthogonal groups O^-(2n,q) and SO^-(2n,q).

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