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 withmulti-dimensional and \(m\)-multiple power Kloosterman sums (for anyfixed \(m\)) over the finite field \(\mathbb{F}_{q}\). Here \(q\) is apower of two. The former codes are dual to a subcode of the binaryhyper-Kloosterman code. Then...
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| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2015
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/65 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| Резюме: | In this paper, we construct two binary linear codes associated withmulti-dimensional and \(m\)-multiple power Kloosterman sums (for anyfixed \(m\)) over the finite field \(\mathbb{F}_{q}\). Here \(q\) is apower of two. The former codes are dual to a subcode of the binaryhyper-Kloosterman code. Then we obtain two recursive formulas forthe power moments of multi-dimensional Kloosterman sums and for the\(m\)-multiple power moments of Kloosterman sums in terms of thefrequencies of weights in the respective codes. This is done viaPless power moment identity and yields, in the case of power momentsof multi-dimensional Kloosterman sums, much simpler recursiveformulas than those associated with finite special linear groupsobtained previously. |
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