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

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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2015
1. Verfasser: Kim, D.S.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2015
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/154253
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren: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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862732656205103104
author Kim, D.S.
author_facet Kim, D.S.
citation_txt 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.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description 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.
first_indexed 2025-12-07T19:33:14Z
format Article
fulltext
id nasplib_isofts_kiev_ua-123456789-154253
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T19:33:14Z
publishDate 2015
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Kim, D.S.
2019-06-15T11:49:34Z
2019-06-15T11:49:34Z
2015
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.
1726-3255
2010 MSC:11T23, 20G40, 94B05.
https://nasplib.isofts.kiev.ua/handle/123456789/154253
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.
This work was supported by National Research Foundation of Korea Grant fundedby the Korean Government 2009-0072514.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
Article
published earlier
spellingShingle Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
Kim, D.S.
title Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
title_full Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
title_fullStr Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
title_full_unstemmed Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
title_short Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums
title_sort recursive formulas generating power moments of multi-dimensional kloosterman sums and m-multiple power moments of kloosterman sums
url https://nasplib.isofts.kiev.ua/handle/123456789/154253
work_keys_str_mv AT kimds recursiveformulasgeneratingpowermomentsofmultidimensionalkloostermansumsandmmultiplepowermomentsofkloostermansums