{"id":"https://openalex.org/W2086769359","doi":"https://doi.org/10.1109/tit.2012.2191477","title":"Finding a Basis Conversion Matrix Using a Polynomial Basis Derived by a Small Multiplicative Cyclic Group","display_name":"Finding a Basis Conversion Matrix Using a Polynomial Basis Derived by a Small Multiplicative Cyclic Group","publication_year":2012,"publication_date":"2012-03-22","ids":{"openalex":"https://openalex.org/W2086769359","doi":"https://doi.org/10.1109/tit.2012.2191477","mag":"2086769359"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2012.2191477","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2191477","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065515042","display_name":"Yasuyuki Nogami","orcid":"https://orcid.org/0000-0001-6247-0719"},"institutions":[{"id":"https://openalex.org/I163770644","display_name":"Okayama University","ror":"https://ror.org/02pc6pc55","country_code":"JP","type":"education","lineage":["https://openalex.org/I163770644"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Yasuyuki Nogami","raw_affiliation_strings":["Department of Communication Network Engineering, Okayama University, Okayama, Japan","[Department of Communication Network Engineering, Okayama University, Okayama, Japan]"],"affiliations":[{"raw_affiliation_string":"Department of Communication Network Engineering, Okayama University, Okayama, Japan","institution_ids":["https://openalex.org/I163770644"]},{"raw_affiliation_string":"[Department of Communication Network Engineering, Okayama University, Okayama, Japan]","institution_ids":["https://openalex.org/I163770644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100850733","display_name":"Hidehiro Kato","orcid":null},"institutions":[{"id":"https://openalex.org/I163770644","display_name":"Okayama University","ror":"https://ror.org/02pc6pc55","country_code":"JP","type":"education","lineage":["https://openalex.org/I163770644"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hidehiro Kato","raw_affiliation_strings":["Department of Communication Network Engineering, Okayama University, Okayama, Japan","[Department of Communication Network Engineering, Okayama University, Okayama, Japan]"],"affiliations":[{"raw_affiliation_string":"Department of Communication Network Engineering, Okayama University, Okayama, Japan","institution_ids":["https://openalex.org/I163770644"]},{"raw_affiliation_string":"[Department of Communication Network Engineering, Okayama University, Okayama, Japan]","institution_ids":["https://openalex.org/I163770644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044041432","display_name":"Kenta Nekado","orcid":null},"institutions":[{"id":"https://openalex.org/I163770644","display_name":"Okayama University","ror":"https://ror.org/02pc6pc55","country_code":"JP","type":"education","lineage":["https://openalex.org/I163770644"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kenta Nekado","raw_affiliation_strings":["Department of Communication Network Engineering, Okayama University, Okayama, Japan","[Department of Communication Network Engineering, Okayama University, Okayama, Japan]"],"affiliations":[{"raw_affiliation_string":"Department of Communication Network Engineering, Okayama University, Okayama, Japan","institution_ids":["https://openalex.org/I163770644"]},{"raw_affiliation_string":"[Department of Communication Network Engineering, Okayama University, Okayama, Japan]","institution_ids":["https://openalex.org/I163770644"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029372795","display_name":"Satoshi Uehara","orcid":"https://orcid.org/0000-0002-1467-5047"},"institutions":[{"id":"https://openalex.org/I17056963","display_name":"The University of Kitakyushu","ror":"https://ror.org/03mfefw72","country_code":"JP","type":"education","lineage":["https://openalex.org/I17056963"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Satoshi Uehara","raw_affiliation_strings":["Department of Information and Media Engineering, University of Kitakyushu, Fukuoka, Japan","[Department of Information and Media Engineering, University of Kitakyushu, Fukuoka, Japan]"],"affiliations":[{"raw_affiliation_string":"Department of Information and Media Engineering, University of Kitakyushu, Fukuoka, Japan","institution_ids":["https://openalex.org/I17056963"]},{"raw_affiliation_string":"[Department of Information and Media Engineering, University of Kitakyushu, Fukuoka, Japan]","institution_ids":["https://openalex.org/I17056963"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113855018","display_name":"Yoshitaka Morikawa","orcid":null},"institutions":[{"id":"https://openalex.org/I163770644","display_name":"Okayama University","ror":"https://ror.org/02pc6pc55","country_code":"JP","type":"education","lineage":["https://openalex.org/I163770644"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yoshitaka Morikawa","raw_affiliation_strings":["Department of Communication Network Engineering, Okayama University, Okayama, Japan","[Department of Communication Network Engineering, Okayama University, Okayama, Japan]"],"affiliations":[{"raw_affiliation_string":"Department of Communication Network Engineering, Okayama University, Okayama, Japan","institution_ids":["https://openalex.org/I163770644"]},{"raw_affiliation_string":"[Department of Communication Network Engineering, Okayama University, Okayama, Japan]","institution_ids":["https://openalex.org/I163770644"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5065515042"],"corresponding_institution_ids":["https://openalex.org/I163770644"],"apc_list":null,"apc_paid":null,"fwci":1.4211,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87526636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"58","issue":"7","first_page":"4936","last_page":"4947"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9879999756813049,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.982200026512146,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7656348943710327},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6300991773605347},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5634389519691467},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5433709025382996},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5332939624786377},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5020368099212646},{"id":"https://openalex.org/keywords/gr\u00f6bner-basis","display_name":"Gr\u00f6bner basis","score":0.488045334815979},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.47873303294181824},{"id":"https://openalex.org/keywords/multiplicative-group","display_name":"Multiplicative group","score":0.4497527778148651},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43414780497550964},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.41711705923080444},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.40107646584510803},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3935641646385193},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.26402777433395386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2327284812927246},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.17209243774414062},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1216217577457428}],"concepts":[{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7656348943710327},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6300991773605347},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5634389519691467},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5433709025382996},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5332939624786377},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5020368099212646},{"id":"https://openalex.org/C198082693","wikidata":"https://www.wikidata.org/wiki/Q1551631","display_name":"Gr\u00f6bner basis","level":3,"score":0.488045334815979},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.47873303294181824},{"id":"https://openalex.org/C92788228","wikidata":"https://www.wikidata.org/wiki/Q3777923","display_name":"Multiplicative group","level":3,"score":0.4497527778148651},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43414780497550964},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.41711705923080444},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.40107646584510803},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3935641646385193},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26402777433395386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2327284812927246},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.17209243774414062},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1216217577457428},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2012.2191477","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2012.2191477","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1520091057","https://openalex.org/W1551781172","https://openalex.org/W1553314411","https://openalex.org/W1556920856","https://openalex.org/W1610688607","https://openalex.org/W1869939343","https://openalex.org/W1978030427","https://openalex.org/W1999637406","https://openalex.org/W2021553056","https://openalex.org/W2022014550","https://openalex.org/W2024260996","https://openalex.org/W2032603633","https://openalex.org/W2067565517","https://openalex.org/W2117788596","https://openalex.org/W2149174385","https://openalex.org/W2162279707","https://openalex.org/W2196559987","https://openalex.org/W2752853835","https://openalex.org/W2752908210","https://openalex.org/W3151140615","https://openalex.org/W4285719527","https://openalex.org/W6639129902","https://openalex.org/W6682116788"],"related_works":["https://openalex.org/W4380051813","https://openalex.org/W4221139454","https://openalex.org/W2055878129","https://openalex.org/W2062309499","https://openalex.org/W2089038681","https://openalex.org/W2283856749","https://openalex.org/W1983651862","https://openalex.org/W2258462132","https://openalex.org/W2127459735","https://openalex.org/W4300947056"],"abstract_inverted_index":{"Several":[0],"methods":[1],"for":[2,120,140],"finding":[3,141],"a":[4,42,82,99,106,142],"basis":[5,28,102,143],"conversion":[6,144],"matrix":[7],"between":[8],"two":[9],"different":[10],"bases":[11],"in":[12,50,90,103,111],"an":[13],"extension":[14,93],"field":[15,45,94],"have":[16,57],"been":[17,58],"proposed.":[18],"Among":[19],"them,":[20],"the":[21,33,52,71,91,118,121,132,137],"one":[22],"based":[23],"on":[24,31],"Gauss":[25],"period":[26],"normal":[27],"(GNB)":[29],"is":[30],"average":[32],"most":[34],"efficient.":[35],"However,":[36],"since":[37],"it":[38],"needs":[39],"to":[40,76],"construct":[41],"certain":[43,100,107],"tower":[44],",":[46,95],"some":[47],"inefficient":[48,66],"cases":[49,67],"which":[51],"towering":[53,122],"degree":[54,123],"becomes":[55],"large":[56],"reported.":[59],"This":[60,113],"paper":[61],"first":[62],"determines":[63],"that":[64,84,131],"such":[65],"are":[68],"caused":[69],"by":[70,105],"GNB":[72,89],"condition.":[73],"In":[74,125],"order":[75],"overcome":[77],"this":[78],"inefficiency,":[79],"we":[80],"propose":[81],"method":[83,134],"does":[85],"not":[86],"use":[87],"any":[88],"target":[92],"but":[96],"instead":[97],"uses":[98],"polynomial":[101],"derived":[104],"small":[108],"cyclic":[109],"group":[110],".":[112,124],"causes":[114],"re-":[115],"laxation":[116],"of":[117],"condition":[119],"addition,":[126],"our":[127],"experimental":[128],"results":[129],"show":[130],"proposed":[133],"substantially":[135],"accelerates":[136],"computation":[138],"time":[139],"matrix.":[145]},"counts_by_year":[{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}