{"id":"https://openalex.org/W3214340774","doi":"https://doi.org/10.1109/tit.2021.3125988","title":"Algorithms for the Minimal Rational Fraction Representation of Sequences Revisited","display_name":"Algorithms for the Minimal Rational Fraction Representation of Sequences Revisited","publication_year":2021,"publication_date":"2021-11-08","ids":{"openalex":"https://openalex.org/W3214340774","doi":"https://doi.org/10.1109/tit.2021.3125988","mag":"3214340774"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3125988","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3125988","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/A5100615417","display_name":"Jun Che","orcid":"https://orcid.org/0000-0003-0013-3340"},"institutions":[{"id":"https://openalex.org/I4210132990","display_name":"State Key Laboratory of Cryptology","ror":"https://ror.org/02pn5rj08","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210132990"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Che","raw_affiliation_strings":["College of Computer Science and Technology, Qingdao University, Qingdao, China","State Key Laboratory of Cryptology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-0013-3340","affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Qingdao University, Qingdao, China","institution_ids":[]},{"raw_affiliation_string":"State Key Laboratory of Cryptology, Beijing, China","institution_ids":["https://openalex.org/I4210132990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020719348","display_name":"Chengliang Tian","orcid":"https://orcid.org/0000-0002-2474-910X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chengliang Tian","raw_affiliation_strings":["College of Computer Science and Technology, Qingdao University, Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0002-2474-910X","affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Qingdao University, Qingdao, China","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030208871","display_name":"Yupeng Jiang","orcid":"https://orcid.org/0000-0003-1347-2560"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yupeng Jiang","raw_affiliation_strings":["School of Cyber Science and Technology, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1347-2560","affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5030897046","display_name":"Guangwu Xu","orcid":"https://orcid.org/0000-0001-6200-3264"},"institutions":[{"id":"https://openalex.org/I154099455","display_name":"Shandong University","ror":"https://ror.org/0207yh398","country_code":"CN","type":"education","lineage":["https://openalex.org/I154099455"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guangwu Xu","raw_affiliation_strings":["School of Cyber Science and Technology, Shandong University (Qingdao), Qingdao, China"],"raw_orcid":"https://orcid.org/0000-0001-6200-3264","affiliations":[{"raw_affiliation_string":"School of Cyber Science and Technology, Shandong University (Qingdao), Qingdao, China","institution_ids":["https://openalex.org/I154099455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1399,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.57956355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"2","first_page":"1316","last_page":"1328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9990000128746033,"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":0.9984999895095825,"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/representation","display_name":"Representation (politics)","score":0.4864508807659149},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.47184041142463684},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46634194254875183},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4421427249908447},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43724897503852844},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42889201641082764},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.41162213683128357},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3755626678466797},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.17406177520751953}],"concepts":[{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4864508807659149},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.47184041142463684},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46634194254875183},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4421427249908447},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43724897503852844},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42889201641082764},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.41162213683128357},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3755626678466797},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.17406177520751953},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2021.3125988","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3125988","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/G172355800","display_name":null,"funder_award_id":"61702294","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2929259477","display_name":null,"funder_award_id":"2016-MS-23","funder_id":"https://openalex.org/F4320321133","funder_display_name":"Chinese Academy of Sciences"},{"id":"https://openalex.org/G5080729982","display_name":null,"funder_award_id":"2019JZZY010133","funder_id":"https://openalex.org/F4320313895","funder_display_name":"Department of Science and Technology of Shandong Province"},{"id":"https://openalex.org/G5653340552","display_name":null,"funder_award_id":"2018YFA0704702","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"}],"funders":[{"id":"https://openalex.org/F4320313895","display_name":"Department of Science and Technology of Shandong Province","ror":"https://ror.org/01b9fvd84"},{"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"},{"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":11,"referenced_works":["https://openalex.org/W1499237070","https://openalex.org/W1584542188","https://openalex.org/W2027487202","https://openalex.org/W2116269747","https://openalex.org/W2146561088","https://openalex.org/W2160707732","https://openalex.org/W2162442687","https://openalex.org/W2163925910","https://openalex.org/W2166147911","https://openalex.org/W2331624694","https://openalex.org/W2984938533"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W1595229445","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W2963177394","https://openalex.org/W1965815883","https://openalex.org/W4313359513","https://openalex.org/W763418848"],"abstract_inverted_index":{"Given":[0],"a":[1,50,97,137,151,229],"binary":[2],"sequence":[3],"with":[4,49,80],"length":[5],"<inline-formula":[6,54,205,212],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,55,130,161,190,206,213],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[8,56,207,214],"<tex-math":[9,57,208,215],"notation=\"LaTeX\">$n$":[10],"</tex-math></inline-formula>":[11,62,210,220],",":[12],"determining":[13],"its":[14],"minimal":[15,105],"rational":[16,46],"fraction":[17],"representation":[18],"(MRFR)":[19],"has":[20],"important":[21],"applications":[22],"in":[23,174],"the":[24,81,89,104,121,141,175,181,198,223,235],"design":[25],"and":[26,40,75,99,153,179],"cryptanalysis":[27],"of":[28,35,53,91,140,201],"stream":[29],"ciphers.":[30],"There":[31],"are":[32],"many":[33],"studies":[34],"this":[36,65,69],"problem":[37,70,90],"since":[38],"Klapper":[39],"Goresky":[41],"first":[42],"introduced":[43],"an":[44],"adaptive":[45,74,124],"approximation":[47],"algorithm":[48,125,145,158,187,203],"time":[51,199],"complexity":[52,200],"notation=\"LaTeX\">$O(n^{2}\\log":[58],"n\\log":[59],"\\log":[60,218],"n)$":[61,219],".":[63,133],"In":[64],"paper,":[66],"we":[67,84,95,149,166,195],"revisit":[68],"by":[71,112,127,135,177,183,221],"considering":[72],"both":[73],"non-adaptive":[76,172],"efficient":[77],"algorithms.":[78],"Compared":[79],"state-of-art":[82],"methods,":[83],"make":[85],"several":[86],"contributions":[87],"to":[88,119,211,238],"finding":[92],"MRFR.":[93],"Firstly,":[94],"find":[96],"general":[98],"precise":[100],"recursive":[101],"relationship":[102],"between":[103],"bases":[106],"for":[107,146],"two":[108],"adjacent":[109],"lattices":[110],"generated":[111],"successive":[113],"truncation":[114],"sequences.":[115],"This":[116],"enables":[117],"us":[118],"improve":[120],"currently":[122],"fastest":[123],"proposed":[126],"Li":[128],"<italic":[129,160,189],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">et":[131],"al.</i>":[132],"Secondly,":[134],"optimizing":[136],"time-consuming":[138],"step":[139],"well-known":[142],"Lagrange":[143],"reduction":[144],"2-dimensional":[147],"lattices,":[148],"obtain":[150],"non-adaptive,":[152],"yet":[154],"practically":[155],"faster":[156],"MRFR-solving":[157],"named":[159,188],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">global</i>":[162],"Euclidean":[163,186,192],"algorithm.":[164,193,225],"Thirdly,":[165],"identify":[167],"theoretical":[168,241],"flaws":[169],"on":[170,234],"some":[171],"methods":[173],"literature":[176],"counter-examples":[178],"correct":[180],"problems":[182],"designing":[184],"modified":[185],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">partial</i>":[191],"Meanwhile,":[194],"further":[196],"reduce":[197],"existing":[202],"from":[204],"notation=\"LaTeX\">$O(n^{2})$":[209],"notation=\"LaTeX\">$O(n\\log":[216],"^{2}n\\log":[217],"invoking":[222],"half-gcd":[224],"We":[226],"also":[227],"conduct":[228],"comprehensive":[230],"experimental":[231],"comparative":[232],"analysis":[233],"above":[236],"algorithms":[237],"validate":[239],"our":[240],"analysis.":[242]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
