{"id":"https://openalex.org/W2041716860","doi":"https://doi.org/10.1109/tit.1986.1057152","title":"Normal basis of finite fieldGF(2^m)(Corresp.)","display_name":"Normal basis of finite fieldGF(2^m)(Corresp.)","publication_year":1986,"publication_date":"1986-03-01","ids":{"openalex":"https://openalex.org/W2041716860","doi":"https://doi.org/10.1109/tit.1986.1057152","mag":"2041716860"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1986.1057152","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057152","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/A5111730123","display_name":"Din Pei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Din Pei","raw_affiliation_strings":["Institute of Applied Mathematics, Academia Sinica, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics, Academia Sinica, Beijing, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071933387","display_name":"C. Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I1334627681","display_name":"Jet Propulsion Laboratory","ror":"https://ror.org/027k65916","country_code":"US","type":"facility","lineage":["https://openalex.org/I122411786","https://openalex.org/I1334627681","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. Wang","raw_affiliation_strings":["Communications Systems Research Section, Jet Propulsion Laboratory, Pasadena, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Communications Systems Research Section, Jet Propulsion Laboratory, Pasadena, CA, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069419916","display_name":"J. K. Omura","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Omura","raw_affiliation_strings":["Electrical Engineering Department, School of Engineering and Applied Science, University of California, Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, School of Engineering and Applied Science, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6331,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.86502623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"32","issue":"2","first_page":"285","last_page":"287"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9972000122070312,"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":0.9972000122070312,"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":0.9796000123023987,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9121000170707703,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.7556848526000977},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.726017951965332},{"id":"https://openalex.org/keywords/normal-basis","display_name":"Normal basis","score":0.6150853633880615},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5965203642845154},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.5713532567024231},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5107884407043457},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.4679970145225525},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38331663608551025},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36498796939849854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34112516045570374},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.26835548877716064},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22935903072357178}],"concepts":[{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.7556848526000977},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.726017951965332},{"id":"https://openalex.org/C205567592","wikidata":"https://www.wikidata.org/wiki/Q3527199","display_name":"Normal basis","level":3,"score":0.6150853633880615},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5965203642845154},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.5713532567024231},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5107884407043457},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.4679970145225525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38331663608551025},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36498796939849854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34112516045570374},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.26835548877716064},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22935903072357178},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1986.1057152","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1986.1057152","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W2076775070","https://openalex.org/W2182112064","https://openalex.org/W2334439626"],"related_works":["https://openalex.org/W2098343516","https://openalex.org/W2028633248","https://openalex.org/W2587136861","https://openalex.org/W2914281158","https://openalex.org/W3128023985","https://openalex.org/W2186975062","https://openalex.org/W2142116768","https://openalex.org/W172172592","https://openalex.org/W1528972180","https://openalex.org/W4248505260"],"abstract_inverted_index":{"Massey":[0],"and":[1,37,64],"Omura":[2],"recently":[3],"developed":[4],"a":[5,21,47,71,77,81],"new":[6],"multiplication":[7,27],"algorithm":[8,19],"for":[9,42],"Galois":[10],"fields":[11],"based":[12],"on":[13],"the":[14,32,51,85],"normal":[15,48,82],"basis":[16,49,83],"representation.":[17],"This":[18,74],"shows":[20],"much":[22],"simpler":[23],"way":[24,78],"to":[25,45,79],"perform":[26],"in":[28,50,84],"finite":[29],"field":[30,52],"than":[31],"conventional":[33],"method.":[34],"The":[35],"necessary":[36],"sufficient":[38],"conditions":[39],"are":[40],"presented":[41],"an":[43],"element":[44],"generate":[46],"GF":[53],"<tex":[54,59,65],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[55,60,66],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(2^{m})</tex>":[56],",":[57],"where":[58],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m":[61],"=":[62],"2^{k}p^{n}</tex>":[63],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p^{n}</tex>":[67],"has":[68],"two":[69],"as":[70],"primitive":[72],"root.":[73],"result":[75],"provides":[76],"find":[80],"field.":[86]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}