{"id":"https://openalex.org/W1994788939","doi":"https://doi.org/10.1090/s0025-5718-96-00663-1","title":"The coefficients of primitive polynomials over finite fields","display_name":"The coefficients of primitive polynomials over finite fields","publication_year":1996,"publication_date":"1996-01-01","ids":{"openalex":"https://openalex.org/W1994788939","doi":"https://doi.org/10.1090/s0025-5718-96-00663-1","mag":"1994788939"},"language":"lv","primary_location":{"id":"doi:10.1090/s0025-5718-96-00663-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00663-1","pdf_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00663-1/S0025-5718-96-00663-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00663-1/S0025-5718-96-00663-1.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010337849","display_name":"Wen Bao Han","orcid":null},"institutions":[{"id":"https://openalex.org/I126520041","display_name":"University of Science and Technology of China","ror":"https://ror.org/04c4dkn09","country_code":"CN","type":"education","lineage":["https://openalex.org/I126520041","https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wen Bao Han","raw_affiliation_strings":["Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, The People\u00e2\u0080\u0099s Republic of China","Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, The People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, The People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I126520041"]},{"raw_affiliation_string":"Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, The People\u2019s Republic of China","institution_ids":["https://openalex.org/I126520041"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5010337849"],"corresponding_institution_ids":["https://openalex.org/I126520041"],"apc_list":null,"apc_paid":null,"fwci":1.7078,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.86668231,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"65","issue":"213","first_page":"331","last_page":"340"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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/T10849","display_name":"Finite Group Theory Research","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11680","display_name":"Advanced Algebra and Geometry","score":0.9732000231742859,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6651002764701843},{"id":"https://openalex.org/keywords/annotation","display_name":"Annotation","score":0.520700991153717},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42484351992607117},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40729978680610657},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.36274254322052}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6651002764701843},{"id":"https://openalex.org/C2776321320","wikidata":"https://www.wikidata.org/wiki/Q857525","display_name":"Annotation","level":2,"score":0.520700991153717},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42484351992607117},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40729978680610657},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36274254322052}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-96-00663-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00663-1","pdf_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00663-1/S0025-5718-96-00663-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-96-00663-1","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-96-00663-1","pdf_url":"https://www.ams.org/mcom/1996-65-213/S0025-5718-96-00663-1/S0025-5718-96-00663-1.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1994788939.pdf","grobid_xml":"https://content.openalex.org/works/W1994788939.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1489774662","https://openalex.org/W1964043652","https://openalex.org/W1996139403","https://openalex.org/W2041398745","https://openalex.org/W2079788827","https://openalex.org/W2091418330","https://openalex.org/W2165674803","https://openalex.org/W3151140615","https://openalex.org/W4236542016","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2361861616","https://openalex.org/W2263699433","https://openalex.org/W2377979023","https://openalex.org/W2218034408","https://openalex.org/W2392921965","https://openalex.org/W2358755282","https://openalex.org/W1979597421","https://openalex.org/W2007980826"],"abstract_inverted_index":{"For":[0],"<inline-formula":[1,34,50],"content-type=\"math/mathml\">":[2,35,51],"<mml:math":[3,36,52],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[4,37,53],"alttext=\"n":[5],"greater-than-or-equal-to":[6],"7\">":[7],"<mml:semantics>":[8,39,65],"<mml:mrow>":[9,66],"<mml:mi>n</mml:mi>":[10,40],"<mml:mo>":[11],"\u2265":[12],"</mml:mo>":[13],"<mml:mn>7</mml:mn>":[14],"</mml:mrow>":[15,77],"<mml:annotation":[16,41,78],"encoding=\"application/x-tex\">n\\ge":[17],"7</mml:annotation>":[18],"</mml:semantics>":[19,43,83],"</mml:math>":[20,44,84],"</inline-formula>":[21,45,85],",":[22],"we":[23],"prove":[24],"that":[25],"there":[26],"always":[27],"exists":[28],"a":[29,47],"primitive":[30],"polynomial":[31],"of":[32],"degree":[33],"alttext=\"n\">":[38],"encoding=\"application/x-tex\">n</mml:annotation>":[42],"over":[46],"finite":[48],"field":[49],"alttext=\"upper":[54],"F":[55],"Subscript":[56],"q":[57,60],"Baseline":[58],"left-parenthesis":[59],"o":[61],"d":[62,63],"right-parenthesis\">":[64],"<mml:msub>":[67],"<mml:mi>F</mml:mi>":[68],"<mml:mi>q</mml:mi>":[69,73],"</mml:msub>":[70],"<mml:mo":[71,75],"stretchy=\"false\">(</mml:mo>":[72],"<mml:mi>odd</mml:mi>":[74],"stretchy=\"false\">)</mml:mo>":[76],"encoding=\"application/x-tex\">F_q":[79],"(q":[80],"\\operatorname":[81],"{odd})</mml:annotation>":[82],"with":[86],"the":[87],"first":[88],"and":[89],"second":[90],"coefficients":[91],"prescribed":[92],"in":[93],"advance.":[94]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-21T06:05:55.347736","created_date":"2025-10-10T00:00:00"}
