{"id":"https://openalex.org/W7127323606","doi":"https://doi.org/10.1109/tit.2026.3657349","title":"On Many-to-One Mappings Over Finite Fields","display_name":"On Many-to-One Mappings Over Finite Fields","publication_year":2026,"publication_date":"2026-02-03","ids":{"openalex":"https://openalex.org/W7127323606","doi":"https://doi.org/10.1109/tit.2026.3657349"},"language":null,"primary_location":{"id":"doi:10.1109/tit.2026.3657349","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3657349","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/A5100681028","display_name":"Yanbin Zheng","orcid":"https://orcid.org/0009-0009-1177-4515"},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanbin Zheng","raw_affiliation_strings":["School of Mathematical Sciences, Qufu Normal University, Qufu, China"],"raw_orcid":"https://orcid.org/0009-0009-1177-4515","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Qufu, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124963023","display_name":"Yanjin Ding","orcid":null},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanjin Ding","raw_affiliation_strings":["School of Mathematical Sciences, Qufu Normal University, Qufu, China"],"raw_orcid":"https://orcid.org/0009-0003-8953-0138","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Qufu, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124901169","display_name":"Meiying Zhang","orcid":null},"institutions":[{"id":"https://openalex.org/I202126657","display_name":"Qufu Normal University","ror":"https://ror.org/03ceheh96","country_code":"CN","type":"education","lineage":["https://openalex.org/I202126657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Meiying Zhang","raw_affiliation_strings":["School of Mathematical Sciences, Qufu Normal University, Qufu, China"],"raw_orcid":"https://orcid.org/0009-0002-1709-8975","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Qufu Normal University, Qufu, China","institution_ids":["https://openalex.org/I202126657"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109829107","display_name":"PINGZHI YUAN","orcid":null},"institutions":[{"id":"https://openalex.org/I187400657","display_name":"South China Normal University","ror":"https://ror.org/01kq0pv72","country_code":"CN","type":"education","lineage":["https://openalex.org/I187400657"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pingzhi Yuan","raw_affiliation_strings":["School of Mathematical Sciences, South China Normal University, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-6398-0614","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, South China Normal University, Guangzhou, China","institution_ids":["https://openalex.org/I187400657"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5124883403","display_name":"Qiang Wang","orcid":null},"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":"Qiang Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada"],"raw_orcid":"https://orcid.org/0000-0001-5426-2776","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12129576,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"5","first_page":"2734","last_page":"2752"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.5317000150680542,"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":0.5317000150680542,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.2987000048160553,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10849","display_name":"Finite Group Theory Research","score":0.031700000166893005,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.5834000110626221},{"id":"https://openalex.org/keywords/multiplicative-group","display_name":"Multiplicative group","score":0.5648999810218811},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5587000250816345},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4652999937534332},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4300000071525574},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4212999939918518},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4106999933719635}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.66839998960495},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.5834000110626221},{"id":"https://openalex.org/C92788228","wikidata":"https://www.wikidata.org/wiki/Q3777923","display_name":"Multiplicative group","level":3,"score":0.5648999810218811},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5587000250816345},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4652999937534332},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45210000872612},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4300000071525574},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4212999939918518},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4106999933719635},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3939000070095062},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39100000262260437},{"id":"https://openalex.org/C35767895","wikidata":"https://www.wikidata.org/wiki/Q5141583","display_name":"Coincidence point","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.29679998755455017},{"id":"https://openalex.org/C2777404646","wikidata":"https://www.wikidata.org/wiki/Q1057968","display_name":"Finite group","level":3,"score":0.28940001130104065},{"id":"https://openalex.org/C2779483109","wikidata":"https://www.wikidata.org/wiki/Q4681347","display_name":"Additive group","level":3,"score":0.2669999897480011},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.26109999418258667}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2026.3657349","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2026.3657349","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":[{"id":"https://openalex.org/G1248013454","display_name":null,"funder_award_id":"No.2024YFA1013000","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G3066141717","display_name":null,"funder_award_id":"No. 12461103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3520298065","display_name":null,"funder_award_id":"12571103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3832650498","display_name":null,"funder_award_id":"12461103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4501408976","display_name":"Finite Fields and applications in coding theory and cryptography","funder_award_id":"rgpin-2023-04673","funder_id":"https://openalex.org/F4320334593","funder_display_name":"Natural Sciences and Engineering Research Council of Canada"},{"id":"https://openalex.org/G7064572572","display_name":null,"funder_award_id":"RGPIN-2023-04673","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8547002873","display_name":null,"funder_award_id":"No. 12571103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W60111835","https://openalex.org/W1480591395","https://openalex.org/W1553319661","https://openalex.org/W1603865303","https://openalex.org/W1970691708","https://openalex.org/W1971990650","https://openalex.org/W1981642919","https://openalex.org/W1986188895","https://openalex.org/W1990773884","https://openalex.org/W2017453435","https://openalex.org/W2043461949","https://openalex.org/W2087896741","https://openalex.org/W2101226255","https://openalex.org/W2119936466","https://openalex.org/W2138238405","https://openalex.org/W2162765352","https://openalex.org/W2412284786","https://openalex.org/W2477775364","https://openalex.org/W2565912892","https://openalex.org/W2566780797","https://openalex.org/W2728070583","https://openalex.org/W2744871629","https://openalex.org/W2754725950","https://openalex.org/W2778234656","https://openalex.org/W2950403555","https://openalex.org/W2951364057","https://openalex.org/W2963158025","https://openalex.org/W2963169017","https://openalex.org/W2963401056","https://openalex.org/W2963775515","https://openalex.org/W2963971814","https://openalex.org/W2968307249","https://openalex.org/W2972280902","https://openalex.org/W3026514873","https://openalex.org/W3107590701","https://openalex.org/W3127078754","https://openalex.org/W3145381334","https://openalex.org/W3153539719","https://openalex.org/W3195080265","https://openalex.org/W4200021230","https://openalex.org/W4236140721","https://openalex.org/W4280570287","https://openalex.org/W4281256415","https://openalex.org/W4304127749","https://openalex.org/W4307217308","https://openalex.org/W4312413685","https://openalex.org/W4316660712","https://openalex.org/W4366288305","https://openalex.org/W4391805624","https://openalex.org/W4396785736","https://openalex.org/W4400078434","https://openalex.org/W4400770856","https://openalex.org/W4401109005","https://openalex.org/W4403678998","https://openalex.org/W4411016824","https://openalex.org/W4412432654","https://openalex.org/W4415207740","https://openalex.org/W7124828630"],"related_works":[],"abstract_inverted_index":{"We":[0,23],"introduce":[1],"the":[2,14,31,47,54,59,70],"definition":[3],"ofm-to-1":[4,41,98],"mappings":[5,19,27,99,101],"between":[6],"two":[7],"finite":[8],"sets,":[9],"which":[10,43],"unifies":[11],"and":[12,35,45,76],"generalizes":[13],"definitions":[15],"of":[16,30],"2-to-1":[17],"andn-to-1":[18],"in":[20,28,87,89],"recent":[21],"literature.":[22],"also":[24],"characterize":[25],"thesem-to-1":[26],"terms":[29],"generalized":[32],"local":[33],"criterion":[34],"thus":[36],"provide":[37],"three":[38],"generic":[39],"constructions":[40],"mappings,":[42],"unify":[44],"generalize":[46],"previous":[48],"known":[49],"constructions.":[50],"Using":[51],"these":[52],"constructions,":[53],"problem":[55],"whetherxrh(xs)":[56],"ism-to-1":[57],"on":[58,69],"multiplicative":[60],"groupF\u2217qis":[61],"converted":[62],"into":[63],"that":[64],"whether":[65],"an":[66],"associated":[67],"polynomialxr1h(x)s1ism2-to-1":[68],"order":[71],"\u2113":[72,77],"subgroupU\u2113":[73],"ofF\u2217q,":[74],"wherem2=m/(r,s)":[75],"=":[78],"(q\u2212":[79],"1)/s.":[80],"Furthermore,":[81],"them2-to-1":[82],"property":[83],"ofxr1h(x)s1onU\u2113":[84],"is":[85,102],"studied":[86],"detail":[88],"five":[90],"different":[91],"cases.":[92],"In":[93],"addition,":[94],"a":[95],"recursive":[96],"construction":[97],"fromm-to-1":[100],"proposed.":[103]},"counts_by_year":[],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2026-02-04T00:00:00"}