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

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
Автор:	Kim, Dae San
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2015
Теми:	Index terms-recursive formula multi-dimensional Kloosterman sum, 11T23 20G40 94B05
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/65
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Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-65
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-652015-09-28T11:22:08Z Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums Kim, Dae San Index terms-recursive formula, multi-dimensional Kloosterman sum, 11T23, 20G40, 94B05 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. Lugansk National Taras Shevchenko University This work was supported by National Research Foundation of Korea Grant funded by the Korean Government 2009-0072514. 2015-09-28 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/65 Algebra and Discrete Mathematics; Vol 19, No 2 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/65/15 Copyright (c) 2015 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
collection	OJS
language	English
topic	Index terms-recursive formula multi-dimensional Kloosterman sum, 11T23 20G40 94B05
spellingShingle	Index terms-recursive formula multi-dimensional Kloosterman sum, 11T23 20G40 94B05 Kim, Dae San Recursive formulas generating power moments of multi-dimensional Kloosterman sums and $m$-multiple power moments of Kloosterman sums
topic_facet	Index terms-recursive formula multi-dimensional Kloosterman sum, 11T23 20G40 94B05
format	Article
author	Kim, Dae San
author_facet	Kim, Dae San
author_sort	Kim, Dae San
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
description	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.
publisher	Lugansk National Taras Shevchenko University
publishDate	2015
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/65
work_keys_str_mv	AT kimdaesan recursiveformulasgeneratingpowermomentsofmultidimensionalkloostermansumsandmmultiplepowermomentsofkloostermansums
first_indexed	2024-04-12T06:25:20Z
last_indexed	2024-04-12T06:25:20Z
_version_	1796109221100519424

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

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