CODES CONSTRUCTED FROM SYMPLECTIC GROUPS AND RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMS
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In this paper, we construct two in nite families of binary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the symplectic group Sp(2n; q). Here q is a power of two. Then we obtain an in nite family of recursive formulas for the power moments of Kloosterman sums and those of 2-dimensional Kloosterman sums 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 exponential sums over those double cosets related to the evaluations of \Gauss sums" for the symplectic groups Sp(2n; q).
Abstract
In this paper, we construct two in nite families of binary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the symplectic group Sp(2n; q). Here q is a power of two. Then we obtain an in nite family of recursive formulas for the power moments of Kloosterman sums and those of 2-dimensional Kloosterman sums 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 exponential sums over those double cosets related to the evaluations of \Gauss sums" for the symplectic groups Sp(2n; q).
참고문헌 (20)
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