Simple Recursive Formulas Generating Power Moments of Kloosterman Sums

TL;DR

This paper develops recursive formulas for calculating power moments of Kloosterman sums by constructing related binary linear codes and applying the Pless power moment identity, advancing understanding of exponential sums over finite fields.

Contribution

The paper introduces four new recursive formulas for Kloosterman sum moments using binary codes and explicit exponential sum expressions, linking coding theory with exponential sum analysis.

Findings

Derived four recursive formulas for Kloosterman sum moments

Connected exponential sums with binary linear codes

Utilized Pless power moment identity for derivations

Abstract

In this paper, we construct four binary linear codes closely connected with certain exponential sums over the finite field F_q and F_q-{0,1}. Here q is a power of two. Then we obtain four recursive formulas for the power moments of 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 the exponential sums obtained earlier.