{"id":"https://openalex.org/W2028694851","doi":"https://doi.org/10.1007/s10623-010-9476-7","title":"Swan-like results for binomials and trinomials over finite fields of odd characteristic","display_name":"Swan-like results for binomials and trinomials over finite fields of odd characteristic","publication_year":2011,"publication_date":"2011-01-04","ids":{"openalex":"https://openalex.org/W2028694851","doi":"https://doi.org/10.1007/s10623-010-9476-7","mag":"2028694851"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-010-9476-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-010-9476-7","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","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/A5020704458","display_name":"Brandon Hanson","orcid":"https://orcid.org/0000-0003-1144-0987"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"B. Hanson","raw_affiliation_strings":["Department of Mathematics, University of Toronto, Room 6290, 40 St. George St., Toronto, ON, M5S 2E4, Canada","Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Toronto, Room 6290, 40 St. George St., Toronto, ON, M5S 2E4, Canada","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Mathematics, University of Toronto, Toronto, Canada M5S 2E4","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017417125","display_name":"Daniel Panario","orcid":"https://orcid.org/0000-0003-3551-4063"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"D. Panario","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, 1125 Colonel By Dr., Ottawa, ON, K1S 5B6, Canada","School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Dr., Ottawa, ON, K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6#TAB#","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101540757","display_name":"David Thomson","orcid":"https://orcid.org/0000-0003-1895-2459"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"D. Thomson","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, 1125 Colonel By Dr., Ottawa, ON, K1S 5B6, Canada","School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, 1125 Colonel By Dr., Ottawa, ON, K1S 5B6, Canada","institution_ids":["https://openalex.org/I67031392"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, Ottawa, Canada, K1S 5B6#TAB#","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5020704458"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":3.1081,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.91906262,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"61","issue":"3","first_page":"273","last_page":"283"},"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/trinomial","display_name":"Trinomial","score":0.9981884956359863},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.8946447372436523},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6469184160232544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5721553564071655},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5618356466293335},{"id":"https://openalex.org/keywords/prime-power","display_name":"Prime power","score":0.5366588830947876},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45217421650886536},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38434964418411255},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35336458683013916}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.9981884956359863},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.8946447372436523},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6469184160232544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5721553564071655},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5618356466293335},{"id":"https://openalex.org/C174072685","wikidata":"https://www.wikidata.org/wiki/Q1667469","display_name":"Prime power","level":3,"score":0.5366588830947876},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45217421650886536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38434964418411255},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35336458683013916}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-010-9476-7","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-010-9476-7","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","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":14,"referenced_works":["https://openalex.org/W1970042430","https://openalex.org/W1974056070","https://openalex.org/W2006157923","https://openalex.org/W2008432412","https://openalex.org/W2056180212","https://openalex.org/W2060682338","https://openalex.org/W2076334265","https://openalex.org/W2082176354","https://openalex.org/W2085575150","https://openalex.org/W2114118536","https://openalex.org/W2145377683","https://openalex.org/W2266326633","https://openalex.org/W2613956024","https://openalex.org/W2915023553"],"related_works":["https://openalex.org/W2091168784","https://openalex.org/W2329470080","https://openalex.org/W4292667350","https://openalex.org/W2990585382","https://openalex.org/W2466745091","https://openalex.org/W2268838648","https://openalex.org/W2002915086","https://openalex.org/W4226315829","https://openalex.org/W2347195016","https://openalex.org/W1668905268"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}