{"id":"https://openalex.org/W3205168295","doi":"https://doi.org/10.1109/tit.2021.3120841","title":"The Adjacency Graphs of FSRs With Affine Characteristic Functions","display_name":"The Adjacency Graphs of FSRs With Affine Characteristic Functions","publication_year":2021,"publication_date":"2021-10-16","ids":{"openalex":"https://openalex.org/W3205168295","doi":"https://doi.org/10.1109/tit.2021.3120841","mag":"3205168295"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3120841","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3120841","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/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","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":true,"raw_author_name":"Ming Li","raw_affiliation_strings":["State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-6401-2639","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"]}]},{"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":"government","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"]},{"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":false,"raw_author_name":"Dongdai Lin","raw_affiliation_strings":["School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China","State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China","School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China; State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3951-7889","affiliations":[{"raw_affiliation_string":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]},{"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":"School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China; 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/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100775894"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210156404"],"apc_list":null,"apc_paid":null,"fwci":0.14,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.56911729,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"1","first_page":"649","last_page":"658"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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":0.9994000196456909,"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/T12029","display_name":"DNA and Biological Computing","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9951000213623047,"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":0.7697687149047852},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.7083938717842102},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.633954644203186},{"id":"https://openalex.org/keywords/adjacency-matrix","display_name":"Adjacency matrix","score":0.6258924007415771},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49525609612464905},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4940495789051056},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.48852503299713135},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3555331826210022},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.19183000922203064},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10772746801376343}],"concepts":[{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.7697687149047852},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.7083938717842102},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.633954644203186},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.6258924007415771},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49525609612464905},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4940495789051056},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.48852503299713135},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3555331826210022},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.19183000922203064},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10772746801376343}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2021.3120841","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3120841","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/G1882683931","display_name":null,"funder_award_id":"61936008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5039410634","display_name":null,"funder_award_id":"61902393","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5361398898","display_name":null,"funder_award_id":"61872359","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"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W127787461","https://openalex.org/W1480210121","https://openalex.org/W1572464666","https://openalex.org/W1745342855","https://openalex.org/W1979635423","https://openalex.org/W1991303196","https://openalex.org/W2004840676","https://openalex.org/W2009427224","https://openalex.org/W2011693214","https://openalex.org/W2018332397","https://openalex.org/W2041749201","https://openalex.org/W2045874481","https://openalex.org/W2059514976","https://openalex.org/W2062919090","https://openalex.org/W2065220771","https://openalex.org/W2079556185","https://openalex.org/W2113627606","https://openalex.org/W2128522106","https://openalex.org/W2128920661","https://openalex.org/W2129813468","https://openalex.org/W2146438343","https://openalex.org/W2156732823","https://openalex.org/W2200124835","https://openalex.org/W2342814867","https://openalex.org/W2402130259","https://openalex.org/W2558573753","https://openalex.org/W2558656005","https://openalex.org/W2559395863","https://openalex.org/W2563737235","https://openalex.org/W2592025126","https://openalex.org/W2617996708","https://openalex.org/W2622212042","https://openalex.org/W2778304398","https://openalex.org/W2805920467","https://openalex.org/W2893091540","https://openalex.org/W2961176507","https://openalex.org/W2963545007","https://openalex.org/W2969020780","https://openalex.org/W3011787975","https://openalex.org/W6738274233"],"related_works":["https://openalex.org/W4213150077","https://openalex.org/W2369410163","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","https://openalex.org/W2153421018"],"abstract_inverted_index":{"We":[0,14,157],"study":[1,118],"the":[2,20,23,34,42,50,72,82,93,96,101,110,119,123,143,148,167],"adjacency":[3,73,84,105,120],"graphs":[4,74,85,106],"of":[5,26,49,55,75,86,95,104,112,122,164,169,190,208],"feedback":[6],"shift":[7],"registers":[8],"(FSRs)":[9],"with":[10,28,77],"affine":[11,29,56,78],"characteristic":[12,30,79,89,126],"functions.":[13],"first":[15],"show":[16],"that,":[17],"similar":[18],"to":[19,92,147],"linear":[21,43,60,144],"case,":[22],"output":[24],"sequences":[25],"FSRs":[27,76,87],"functions":[31,80,90],"also":[32],"have":[33],"direct":[35],"sum":[36],"decompositions.":[37],"The":[38],"only":[39],"difference":[40],"from":[41],"case":[44],"is":[45,52,128,142,175,187,204],"that":[46,159],"one":[47],"component":[48],"decomposition":[51],"a":[53,69,188,206],"family":[54],"sequences,":[57],"rather":[58],"than":[59,178,195],"sequences.":[61],"Then,":[62],"based":[63],"on":[64],"this":[65,165],"fact,":[66],"we":[67,116],"give":[68],"relationship":[70,99],"between":[71],"and":[81,107,192],"generalized":[83],"whose":[88,125],"correspond":[91],"components":[94],"decomposition.":[97],"This":[98],"establishes":[100],"algebraic":[102],"structure":[103],"greatly":[108],"simplifies":[109],"calculation":[111],"them.":[113],"At":[114],"last,":[115],"especially":[117],"graph":[121],"FSR":[124],"function":[127,145],"<inline-formula":[129,136,150,181,198],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[130,137,151,182,199],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[131,138,152,183,200],"<tex-math":[132,139,153,184,201],"notation=\"LaTeX\">$q_{k}(x)+1$":[133],"</tex-math></inline-formula>":[134,141,155,186,203],"where":[135],"notation=\"LaTeX\">$q_{k}(x)$":[140],"corresponding":[146],"polynomial":[149],"notation=\"LaTeX\">$(1+x)^{k}$":[154],".":[156],"prove":[158],"for":[160],"any":[161],"two":[162],"cycles":[163],"FSR,":[166],"number":[168],"conjugate":[170],"pairs":[171],"shared":[172],"by":[173],"them":[174],"no":[176,193],"more":[177,194],"4":[179],"if":[180,197],"notation=\"LaTeX\">$k$":[185,202],"power":[189,207],"2,":[191],"2":[196],"not":[205],"2.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}