{"id":"https://openalex.org/W1990605160","doi":"https://doi.org/10.1016/s0019-9958(67)91016-9","title":"On the solution of algebraic equations over finite fields","display_name":"On the solution of algebraic equations over finite fields","publication_year":1967,"publication_date":"1967-06-01","ids":{"openalex":"https://openalex.org/W1990605160","doi":"https://doi.org/10.1016/s0019-9958(67)91016-9","mag":"1990605160"},"language":"en","primary_location":{"id":"doi:10.1016/s0019-9958(67)91016-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0019-9958(67)91016-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210192454","display_name":"Information and Control","issn_l":"0019-9958","issn":["0019-9958","1878-2981"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319955","host_organization_name":"Academic Press","host_organization_lineage":["https://openalex.org/P4310319955","https://openalex.org/P4310320990"],"host_organization_lineage_names":["Academic Press","Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Control","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/A5090352309","display_name":"Elwyn R. Berlekamp","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":"E.R. Berlekamp","raw_affiliation_strings":["Jet Propulsion Laboratory, Pasadena, California 91103, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, Pasadena, California 91103, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110097877","display_name":"Howard Rumsey","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":"H. Rumsey","raw_affiliation_strings":["Jet Propulsion Laboratory, Pasadena, California 91103, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, Pasadena, California 91103, USA","institution_ids":["https://openalex.org/I1334627681"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110919677","display_name":"G. Solomon","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":"G. Solomon","raw_affiliation_strings":["Jet Propulsion Laboratory, Pasadena, California 91103, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jet Propulsion Laboratory, Pasadena, California 91103, USA","institution_ids":["https://openalex.org/I1334627681"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I1334627681"],"apc_list":null,"apc_paid":null,"fwci":6.5729,"has_fulltext":false,"cited_by_count":179,"citation_normalized_percentile":{"value":0.95540025,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"10","issue":"6","first_page":"553","last_page":"564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6194478869438171},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6167383790016174},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.6089311242103577},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.5641195774078369},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.4501754939556122},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.4411354660987854},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.43282434344291687},{"id":"https://openalex.org/keywords/low-density-parity-check-code","display_name":"Low-density parity-check code","score":0.42213308811187744},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.41966676712036133},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.40693724155426025},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39368775486946106},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2522883415222168},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2414717972278595},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21183687448501587},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09819841384887695}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6194478869438171},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6167383790016174},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.6089311242103577},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.5641195774078369},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.4501754939556122},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.4411354660987854},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.43282434344291687},{"id":"https://openalex.org/C67692717","wikidata":"https://www.wikidata.org/wiki/Q187444","display_name":"Low-density parity-check code","level":3,"score":0.42213308811187744},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.41966676712036133},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.40693724155426025},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39368775486946106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2522883415222168},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2414717972278595},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21183687448501587},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09819841384887695},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/s0019-9958(67)91016-9","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0019-9958(67)91016-9","pdf_url":null,"source":{"id":"https://openalex.org/S4210192454","display_name":"Information and Control","issn_l":"0019-9958","issn":["0019-9958","1878-2981"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319955","host_organization_name":"Academic Press","host_organization_lineage":["https://openalex.org/P4310319955","https://openalex.org/P4310320990"],"host_organization_lineage_names":["Academic Press","Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Information and Control","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":7,"referenced_works":["https://openalex.org/W1984088659","https://openalex.org/W1996310087","https://openalex.org/W2064759901","https://openalex.org/W2091985031","https://openalex.org/W2335771728","https://openalex.org/W3141855661","https://openalex.org/W6649379003"],"related_works":["https://openalex.org/W2903058006","https://openalex.org/W2102374550","https://openalex.org/W2047069332","https://openalex.org/W2352157218","https://openalex.org/W4213381250","https://openalex.org/W2806845321","https://openalex.org/W2393084694","https://openalex.org/W2336709242","https://openalex.org/W4318215366","https://openalex.org/W2372031134"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":12},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":14},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
