{"id":"https://openalex.org/W2559395863","doi":"https://doi.org/10.1109/tit.2016.2634420","title":"The Adjacency Graphs of LFSRs With Primitive-Like Characteristic Polynomials","display_name":"The Adjacency Graphs of LFSRs With Primitive-Like Characteristic Polynomials","publication_year":2016,"publication_date":"2016-12-02","ids":{"openalex":"https://openalex.org/W2559395863","doi":"https://doi.org/10.1109/tit.2016.2634420","mag":"2559395863"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2016.2634420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2634420","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/A5100775894","display_name":"Ming Li","orcid":"https://orcid.org/0000-0002-6401-2639"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ming Li","raw_affiliation_strings":["University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"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/A5100775894"],"corresponding_institution_ids":["https://openalex.org/I4210165038"],"apc_list":null,"apc_paid":null,"fwci":2.9993,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.93033323,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"63","issue":"2","first_page":"1325","last_page":"1335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9944999814033508,"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":0.9933000206947327,"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/adjacency-list","display_name":"Adjacency list","score":0.7309565544128418},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6170591115951538},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5631790161132812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5522857308387756},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5129875540733337},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.42661598324775696},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4200584292411804},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.33993953466415405},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12744343280792236}],"concepts":[{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.7309565544128418},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6170591115951538},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5631790161132812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5522857308387756},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5129875540733337},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.42661598324775696},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4200584292411804},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.33993953466415405},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12744343280792236},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2016.2634420","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2016.2634420","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/G6314305349","display_name":null,"funder_award_id":"XDA06010701","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G6335640023","display_name":null,"funder_award_id":"61379139","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8954342705","display_name":null,"funder_award_id":"11526215","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/F4320321133","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1480210121","https://openalex.org/W1827311732","https://openalex.org/W1966042291","https://openalex.org/W1978493550","https://openalex.org/W1991303196","https://openalex.org/W2007453203","https://openalex.org/W2007799433","https://openalex.org/W2011693214","https://openalex.org/W2018332397","https://openalex.org/W2035511639","https://openalex.org/W2041749201","https://openalex.org/W2058219874","https://openalex.org/W2059514976","https://openalex.org/W2062919090","https://openalex.org/W2076568250","https://openalex.org/W2129813468","https://openalex.org/W2133087726","https://openalex.org/W2146438343","https://openalex.org/W2200124835","https://openalex.org/W2292044371","https://openalex.org/W2402130259","https://openalex.org/W2592570088","https://openalex.org/W2613956024","https://openalex.org/W3199563021","https://openalex.org/W4234875403","https://openalex.org/W4243205024","https://openalex.org/W6801293233"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","https://openalex.org/W2982430984","https://openalex.org/W2059018062","https://openalex.org/W2604585036","https://openalex.org/W2078477160","https://openalex.org/W1989103179","https://openalex.org/W1991172810","https://openalex.org/W125803343","https://openalex.org/W2117632582"],"abstract_inverted_index":{"We":[0],"consider":[1],"the":[2,6,16,60,71,95,100,106,110],"adjacency":[3,54,89,101],"graphs":[4,55,102],"of":[5,15,35,63,94,103,109,124],"linear":[7],"feedback":[8],"shift":[9],"registers":[10],"(LFSRs)":[11],"with":[12,105],"characteristic":[13,107],"polynomials":[14,108],"form":[17,111],"<inline-formula":[18,26,39,64,112],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[19,27,40,65,113],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[20,28,41,66,114],"<tex-math":[21,29,42,67,115],"notation=\"LaTeX\">$l(x)p(x)$":[22],"</tex-math></inline-formula>":[23,31,44,69,117],",":[24,118],"where":[25],"notation=\"LaTeX\">$l(x)$":[30,68],"is":[32,45,50],"a":[33,46,83,121],"polynomial":[34],"small":[36],"degree":[37],"and":[38,70,119],"notation=\"LaTeX\">$p(x)$":[43],"primitive":[47],"polynomial.":[48],"It":[49],"shown":[51],"that":[52],"their":[53,88],"are":[56],"closely":[57],"related":[58],"to":[59,86],"association":[61],"graph":[62],"cyclotomic":[72],"numbers":[73],"over":[74],"finite":[75],"fields.":[76],"By":[77],"using":[78],"this":[79],"connection,":[80],"we":[81,97],"give":[82],"unified":[84],"method":[85],"determine":[87],"graphs.":[90],"As":[91],"an":[92],"application":[93],"method,":[96],"explicitly":[98],"calculate":[99],"LFSRs":[104],"notation=\"LaTeX\">$(1+x+x^{3}+x^{4})p(x)$":[116],"construct":[120],"large":[122],"class":[123],"De":[125],"Bruijn":[126],"sequences":[127],"from":[128],"them.":[129]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}