{"id":"https://openalex.org/W2791091839","doi":"https://doi.org/10.1109/tit.2018.2796127","title":"Lower and Upper Bounds on the Density of Irreducible NFSRs","display_name":"Lower and Upper Bounds on the Density of Irreducible NFSRs","publication_year":2018,"publication_date":"2018-01-22","ids":{"openalex":"https://openalex.org/W2791091839","doi":"https://doi.org/10.1109/tit.2018.2796127","mag":"2791091839"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2796127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2796127","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/A5030208871","display_name":"Yupeng Jiang","orcid":"https://orcid.org/0000-0003-1347-2560"},"institutions":[{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yupeng Jiang","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","[State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China]"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]},{"raw_affiliation_string":"[State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China]","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008820992","display_name":"Dongdai Lin","orcid":"https://orcid.org/0000-0002-3951-7889"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210156404","display_name":"Institute of Information Engineering","ror":"https://ror.org/04r53se39","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210156404"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongdai Lin","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","[State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China]"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]},{"raw_affiliation_string":"[State Key Laboratory of Information Security Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China]","institution_ids":["https://openalex.org/I4210156404","https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5030208871"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"],"apc_list":null,"apc_paid":null,"fwci":0.9773,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.81183,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"64","issue":"5","first_page":"3944","last_page":"3952"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9993000030517578,"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":0.9993000030517578,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9980000257492065,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.8582502603530884},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6517417430877686},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5303956270217896},{"id":"https://openalex.org/keywords/tian","display_name":"Tian","score":0.526988685131073},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.48404258489608765},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3923015892505646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.16114690899848938},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09503716230392456},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08332914113998413}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.8582502603530884},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6517417430877686},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5303956270217896},{"id":"https://openalex.org/C2779802804","wikidata":"https://www.wikidata.org/wiki/Q1364799","display_name":"Tian","level":2,"score":0.526988685131073},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.48404258489608765},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3923015892505646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.16114690899848938},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09503716230392456},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08332914113998413},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2018.2796127","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2796127","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/G5304704547","display_name":null,"funder_award_id":"61421120102162112007","funder_id":"https://openalex.org/F4320327655","funder_display_name":"Foundation of Science and Technology on Information Assurance Laboratory"},{"id":"https://openalex.org/G6234306720","display_name":null,"funder_award_id":"61502483","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/F4320327655","display_name":"Foundation of Science and Technology on Information Assurance Laboratory","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1480210121","https://openalex.org/W1827311732","https://openalex.org/W1991353547","https://openalex.org/W2041749201","https://openalex.org/W2058219874","https://openalex.org/W2073504630","https://openalex.org/W2090600233","https://openalex.org/W2263835564","https://openalex.org/W2624893993","https://openalex.org/W2732251371","https://openalex.org/W4234875403"],"related_works":["https://openalex.org/W2381877804","https://openalex.org/W2394172368","https://openalex.org/W2386995406","https://openalex.org/W2367282044","https://openalex.org/W4232991284","https://openalex.org/W2358780700","https://openalex.org/W2368587157","https://openalex.org/W4239304471","https://openalex.org/W2375001374","https://openalex.org/W2369188975"],"abstract_inverted_index":{"A":[0],"nonlinear":[1],"feedback":[2],"shift":[3],"register":[4],"(NFSR)":[5],"of":[6,14,17,20,30,48,68],"n-stage":[7],"is":[8,25,80],"called":[9],"irreducible":[10,49,69],"if,":[11],"the":[12,31,46,66,72],"family":[13],"output":[15],"sequences":[16],"any":[18],"NFSR":[19],"stage":[21],"less":[22,81],"than":[23,82],"$n$":[24],"not":[26],"included":[27],"in":[28,36],"that":[29],"NFSR.":[32],"Tian":[33],"and":[34,59,77],"Qi":[35],"this":[37,52],"paper":[38],"[IEEE-IT,":[39],"2013(6),4006-4012]":[40],"gave":[41],"a":[42],"lower":[43,57,78],"bound":[44,58,64],"on":[45,65],"density":[47,67],"NFSRs.":[50,70],"In":[51],"paper,":[53],"we":[54],"improve":[55],"their":[56],"also":[60],"give":[61],"an":[62],"upper":[63,76],"Moreover,":[71],"gap":[73],"between":[74],"our":[75],"bounds":[79],"0.04.":[83]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}