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...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2015 |
| 1. Verfasser: | |
| 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 |