{"id":"https://openalex.org/W4411720755","doi":"https://doi.org/10.61091/ars163-05","title":"Primitive normal pairs with prescribed traces over finite fields","display_name":"Primitive normal pairs with prescribed traces over finite fields","publication_year":2025,"publication_date":"2025-06-27","ids":{"openalex":"https://openalex.org/W4411720755","doi":"https://doi.org/10.61091/ars163-05"},"language":"en","primary_location":{"id":"doi:10.61091/ars163-05","is_oa":true,"landing_page_url":"https://doi.org/10.61091/ars163-05","pdf_url":"https://combinatorialpress.com/article/ars/Volume%20163/primitive-normal-pairs-with-prescribed-traces-over-finite-fields.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://combinatorialpress.com/article/ars/Volume%20163/primitive-normal-pairs-with-prescribed-traces-over-finite-fields.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102679540","display_name":"Shikhamoni Nath","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shikhamoni Nath","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113903638","display_name":"Arpan Chandra Mazumder","orcid":"https://orcid.org/0009-0005-9527-6150"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arpan Chandra Mazumder","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5036581109","display_name":"Dhiren Kumar Basnet","orcid":"https://orcid.org/0000-0002-9589-9287"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dhiren Kumar Basnet","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20161922,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"163","issue":null,"first_page":"69","last_page":"82"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9977999925613403,"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/T11130","display_name":"Coding theory and cryptography","score":0.9970999956130981,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9810000061988831,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8208224773406982},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5168331265449524},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41476574540138245},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3156856894493103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8208224773406982},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5168331265449524},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41476574540138245},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3156856894493103}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.61091/ars163-05","is_oa":true,"landing_page_url":"https://doi.org/10.61091/ars163-05","pdf_url":"https://combinatorialpress.com/article/ars/Volume%20163/primitive-normal-pairs-with-prescribed-traces-over-finite-fields.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.61091/ars163-05","is_oa":true,"landing_page_url":"https://doi.org/10.61091/ars163-05","pdf_url":"https://combinatorialpress.com/article/ars/Volume%20163/primitive-normal-pairs-with-prescribed-traces-over-finite-fields.pdf","source":{"id":"https://openalex.org/S73158690","display_name":"Ars Combinatoria","issn_l":"0381-7032","issn":["0381-7032","2817-5204"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4323439501","host_organization_name":"Charles Babbage Research Centre","host_organization_lineage":["https://openalex.org/P4323439501"],"host_organization_lineage_names":["Charles Babbage Research Centre"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Ars Combinatoria","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4411720755.pdf","grobid_xml":"https://content.openalex.org/works/W4411720755.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"&lt;p&gt;Let":[0],"&lt;span":[1,12,16,24,30,51,56,60,67,71,75,88,96,99],"class=\"math":[2,13,17,25,31,52,57,61,68,72,76,89,97,100],"inline\"&gt;\\(q\\)&lt;/span&gt;":[3],"be":[4,19],"a":[5,20,38,81],"positive":[6],"integral":[7],"power":[8],"of":[9,44,48],"some":[10,29,85],"prime":[11],"inline\"&gt;\\(p\\)&lt;/span&gt;":[14],"and":[15,70,87,104],"inline\"&gt;\\(\\mathbb{F}_{q^m}\\)&lt;/span&gt;":[18,58],"finite":[21],"field":[22],"with":[23,63,84,107],"inline\"&gt;\\(q^m\\)&lt;/span&gt;":[26],"elements":[27],"for":[28,41,95],"inline\"&gt;\\(m":[32,101],"\\in":[33,78,92],"\\mathbb{N}\\)&lt;/span&gt;.":[34],"Here":[35],"we":[36,111],"establish":[37],"sufficient":[39],"condition":[40],"the":[42,49,120],"existence":[43],"primitive":[45],"normal":[46],"pairs":[47],"type":[50],"inline\"&gt;\\((\\epsilon,":[53],"f(\\epsilon))\\)&lt;/span&gt;":[54],"in":[55,118],"over":[59],"inline\"&gt;\\(\\mathbb{F}_{q}\\)&lt;/span&gt;":[62],"two":[64],"prescribed":[65],"traces,":[66],"inline\"&gt;\\(\\text{Tr}_{{\\mathbb{F}_{q^m}}/{\\mathbb{F}_q}}(\\epsilon)=a\\)&lt;/span&gt;":[69],"inline\"&gt;\\(\\text{Tr}_{{\\mathbb{F}_{q^m}}/{\\mathbb{F}_q}}(f(\\epsilon))=b\\)&lt;/span&gt;,":[73],"where":[74],"inline\"&gt;\\(f(x)":[77],"\\mathbb{F}_{q^m}(x)\\)&lt;/span&gt;":[79],"is":[80],"rational":[82,105],"function":[83],"restrictions":[86],"inline\"&gt;\\(a,":[90],"b":[91],"\\mathbb{F}^*_q\\)&lt;/span&gt;.":[93],"Furthermore,":[94],"inline\"&gt;\\(q=5^k\\)&lt;/span&gt;,":[98],"\\geq":[102],"9\\)&lt;/span&gt;":[103],"functions":[106],"degree":[108],"sum":[109],"4,":[110],"explicitly":[112],"find":[113],"at":[114],"most":[115],"13":[116],"fields":[117],"which":[119],"desired":[121],"pair":[122],"may":[123],"not":[124],"exist.&lt;/p&gt;":[125]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-06-27T00:00:00"}
