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ガロア環上の組合せ数学の研究
https://doi.org/10.24517/00034548
https://doi.org/10.24517/00034548fc3b4c1d-7a3c-45ee-89d9-49db3620079b
名前 / ファイル | ライセンス | アクション |
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SC-PR-YAMADA-M-kaken 2013-4p.pdf (340.9 kB)
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Item type | 報告書 / Research Paper(1) | |||||
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公開日 | 2017-10-05 | |||||
タイトル | ||||||
タイトル | ガロア環上の組合せ数学の研究 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Research on combinatorics over Galois rings | |||||
言語 | ||||||
言語 | jpn | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_18ws | |||||
資源タイプ | research report | |||||
ID登録 | ||||||
ID登録 | 10.24517/00034548 | |||||
ID登録タイプ | JaLC | |||||
著者 |
山田, 美枝子
× 山田, 美枝子 |
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著者別表示 |
Yamada, Mieko
× Yamada, Mieko |
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書誌情報 |
平成24(2012)年度 科学研究費補助金 基盤研究(C) 研究成果報告書 en : 2012 Fiscal Year Final Research Report 巻 2008-2012, p. 4p., 発行日 2013-05-21 |
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出版者 | ||||||
出版者 | 金沢大学数物科学系 | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | 標数が2^t(t:偶数)である任意の拡大のガロア環上に標数2^tのガロア環上の差集合が標数2^t+2 のガロア環の差集合のイデアル部分に埋め込まれているような差集合の系列を構成した.ガロア環に新しい演算を導入し、この演算に関する指標に付随するガウス和が証明に重要な役割を果たしている.さらに同じガロア環上に埋め込み構造を持つReed-Muller codeが存在することを示し、その性質を明らかにした. | |||||
抄録 | ||||||
内容記述タイプ | Abstract | |||||
内容記述 | We constructed infinite families of difference sets over Galois rings of characteristic an even power of 2. The difference set over a Galois ring of characteristic 2^n is embedded in the ideal part of the difference set over a Galois ring of characteristic 2^n+2 . We introduced a new operation in a Galois ring and the Gauss sums associated with the character under this new operation play an important role of the proof. Furthermore, we proved there exist Reed-Muller codes with embedding system and showed several properties of them. | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 研究課題/領域番号:20540014, 研究期間(年度):2008–2012 | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | 出典:研究課題「ガロア環上の組合せ数学の研究」研究課題番号20540014 (KAKEN:科学研究費助成事業データベース(国立情報学研究所)) (https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-20540014/20540014seika/)を加工して作成 |
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著者版フラグ | ||||||
出版タイプ | AM | |||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||
関連URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://kaken.nii.ac.jp/search/?qm=70130226 | |||||
関連名称 | https://kaken.nii.ac.jp/search/?qm=70130226 | |||||
関連URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540014/ | |||||
関連名称 | https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540014/ | |||||
関連URI | ||||||
識別子タイプ | URI | |||||
関連識別子 | https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-20540014/20540014seika/ | |||||
関連名称 | https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-20540014/20540014seika/ |