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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| Date: | 2015 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2015
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/154253 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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