Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums

Dae San Kim

Algebra and discrete mathematics, Tome 19 (2015) no. 2, pp. 213-228.

Résumé

In this paper, we construct two binary linear codes associated with multi-dimensional and $m -$multiple power Kloosterman sums (for any fixed $m$) over the finite field $\mathbb{F}_{q}$. Here $q$ is a power of two. The former codes are dual to a subcode of the binary hyper-Kloosterman code. Then we obtain two recursive formulas for the power moments of multi-dimensional Kloosterman sums and for the $m$-multiple power moments of Kloosterman sums in terms of the frequencies of weights in the respective codes. This is done via Pless power moment identity and yields, in the case of power moments of multi-dimensional Kloosterman sums, much simpler recursive formulas than those associated with finite special linear groups obtained previously.

Détail

Keywords: index terms-recursive formula, multi-dimensional Kloosterman sum, Kloosterman sum, Pless power moment identity, weight distribution.

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