{"created":"2023-07-27T06:44:17.728730+00:00","id":34471,"links":{},"metadata":{"_buckets":{"deposit":"5566a2e9-1cee-4835-a31e-9f74f6e3502d"},"_deposit":{"created_by":3,"id":"34471","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34471"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034471","sets":["2812:2813:2819"]},"author_link":["17387"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2015-06-13","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"4p.","bibliographicVolumeNumber":"2012-04-01 – 2015-03-31","bibliographic_titles":[{"bibliographic_title":"平成26(2014)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2014 Fiscal Year Final Research Report","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{}],"nameIdentifiers":[{},{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"局所体の部分集合の射影像として組合せ構造を捉えるという新しい視点と研究方法を与えた．２進体の整数環のある部分集合をガロア環に射影すると、入れ子構造を持つ差集合の無限系列が得られることを示した．また、標数が4のガロア環にdifference family, Hadamard行列が構成できることを示した．標数が奇素数べきのガロア環については、BCH codeの2エラーまで復号できるアルゴリズムの構築、標数が一般の素数の２乗であるガロア環の差集合族の構成の結果がある．この他、有限体のCayley graphとそのlifting, skew Hadamard 行列の分類の新しい知見等の結果がある．","subitem_description_type":"Abstract"},{"subitem_description":"We gave a new approach and a new perspective on the study of combinatorics, that is,recognizing a combinatorial structure over finite fields and Galois rings as an image of a subset of a local　field by natural projections. We obtained an infinite family of Menon-Hadamard difference sets over Galois rings of characteristic a power of 2 from a subset of 2-adic field by natural projections, which has a　nested structure. Furthermore we showed that there exist difference families and Hadamard matrices over Galois rings of　characteristic 4. For odd characteristics, we constructed a decoding algorithm of BCH codes with at most 2 errors. For a characteristic a square of a prime and an　extension degree 2, we constructed difference families and Hadamard matrices.\nIn addition to the above results, we constructed Cayley graphs and their lifting and provided a new insight of the classification of skew Hadamard matrices over finite fields.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:24540013, 研究期間(年度):2012-04-01 – 2015-03-31","subitem_description_type":"Other"},{"subitem_description":"出典：研究課題「ガロア環の組合せ数学の研究」課題番号24540013\n（KAKEN：科学研究費助成事業データベース（国立情報学研究所）） \n（https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-24540013/24540013seika/）を加工して作成","subitem_description_type":"Other"}]},"item_9_description_5":{"attribute_name":"提供者所属","attribute_value_mlt":[{"subitem_description":"東京女子大学 / 金沢大学理工学域数物科学系","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00034458","subitem_identifier_reg_type":"JaLC"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/search/?qm=70130226"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=70130226","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24540013/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-24540013/","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-24540013/24540013seika/"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-24540013/24540013seika/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-10-05"}],"displaytype":"detail","filename":"SC-PR-YAMADA-M-kaken 2015-4p.pdf","filesize":[{"value":"170.1 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"SC-PR-YAMADA-M-kaken 2015-4p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34471/files/SC-PR-YAMADA-M-kaken 2015-4p.pdf"},"version_id":"bda01ae1-344c-4835-861f-9ab58c0c7afb"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"ガロア環の組合せ数学の研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"ガロア環の組合せ数学の研究"},{"subitem_title":"A study of combinatorics over Galois rings","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2819"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34471","relation_version_is_last":true,"title":["ガロア環の組合せ数学の研究"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T10:46:29.162012+00:00"}