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 code. Then we obtain two recurs...
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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154253 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-154253 |
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| record_format |
dspace |
| spelling |
irk-123456789-1542532019-06-16T01:26:52Z Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums Kim, D.S. 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. 2015 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/154253 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Kim, D.S. |
| spellingShingle |
Kim, D.S. Recursive formulas generating power moments of multi-dimensional Kloosterman sums and m-multiple power moments of Kloosterman sums Algebra and Discrete Mathematics |
| author_facet |
Kim, D.S. |
| author_sort |
Kim, D.S. |
| title |
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_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_sort |
recursive formulas generating power moments of multi-dimensional kloosterman sums and m-multiple power moments of kloosterman sums |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2015 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154253 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:43:32Z |
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