Abstract
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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*This work was supported by the National Research Foundation of Korea grant funded by the Korean Government 2009–0072514.
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Kim, D.S. Ternary codes associated with O −(2n, q) and power moments of kloosterman sums with square arguments* . Lith Math J 51, 507–521 (2011). https://doi.org/10.1007/s10986-011-9144-2
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DOI: https://doi.org/10.1007/s10986-011-9144-2
Keywords
- ternary linear code
- power moment
- Kloosterman sum
- square argument
- Pless power moment identity
- Gauss sum
- orthogonal group
- weight distribution