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

• Published in: Algebra and Discrete Mathematics
• Date: 2015
• Main Author: Kim, D.S.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154253
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums / D.S. Kim // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 2. — С. 213-228 . — Бібліогр.: 18 назв. — англ.

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 Fq. 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.