# Article ID: MTJPAM-D-19-00001

## Title: RECURSIVE FORMULAS GENERATING POWER MOMENTS OF KLOOSTERMAN SUMS: SYMPLECTIC CASE

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-19-00001; Volume 1 / Issue 1 / Year 2019, Pages 77-95

Document Type: Research Paper

Author(s): Dae San Kim a

aDepartment of Mathematics, Sogang University, Seoul 121-742, Korea

Received: 4 July 2019, Accepted: 16 October 2019, Available online: 28 November 2019.

Corresponding Author: Dae San Kim (Email address: dskim@sogang.ac.kr)

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Abstract

In this paper, we construct two infinite 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 infinite 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 sum” for the symplectic groups Sp(2n, q).

Keywords: Kloosterman sum, symplectic group, double cosets, maximal parabolic subgroup, Pless power moment identity, weight distribution

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