{"id":"https://openalex.org/W4210697516","doi":"https://doi.org/10.3390/appliedmath2010005","title":"Rotating Binaries","display_name":"Rotating Binaries","publication_year":2022,"publication_date":"2022-02-03","ids":{"openalex":"https://openalex.org/W4210697516","doi":"https://doi.org/10.3390/appliedmath2010005"},"language":"en","primary_location":{"id":"doi:10.3390/appliedmath2010005","doi":"https://doi.org/10.3390/appliedmath2010005","is_oa":true,"landing_page_url":"https://doi.org/10.3390/appliedmath2010005","pdf_url":"https://www.mdpi.com/2673-9909/2/1/5/pdf?version=1644831784","source":{"id":"https://openalex.org/S4210196797","display_name":"AppliedMath","issn_l":"2673-9909","issn":["2673-9909"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AppliedMath","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2673-9909/2/1/5/pdf?version=1644831784","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040587523","display_name":"Anant Gupta","orcid":"https://orcid.org/0000-0001-9674-3789","observed_orcids":["https://orcid.org/0000-0001-9674-3789"]},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anant Gupta","raw_affiliation_strings":["Georgia Institute of Technology, North Ave NW, Atlanta, GA 30332, USA"],"raw_orcid":"https://orcid.org/0000-0001-9674-3789","affiliations":[{"raw_affiliation_string":"Georgia Institute of Technology, North Ave NW, Atlanta, GA 30332, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080945099","display_name":"Idriss Aberkane","orcid":"https://orcid.org/0000-0002-2534-6978","observed_orcids":["https://orcid.org/0000-0002-2534-6978"]},"institutions":[{"id":"https://openalex.org/I1293226324","display_name":"UNESCO","ror":"https://ror.org/04h4z8k05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1286959531","https://openalex.org/I1293226324","https://openalex.org/I2801247003"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Idriss J. Aberkane","raw_affiliation_strings":["Unesco-Unitwin Complex Systems Digital Campus, ECCE e-Lab, CEDEX, 67081 Strasbourg, France"],"raw_orcid":"https://orcid.org/0000-0002-2534-6978","affiliations":[{"raw_affiliation_string":"Unesco-Unitwin Complex Systems Digital Campus, ECCE e-Lab, CEDEX, 67081 Strasbourg, France","institution_ids":["https://openalex.org/I1293226324"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010378117","display_name":"Sourangshu Ghosh","orcid":"https://orcid.org/0000-0002-4198-9279","observed_orcids":["https://orcid.org/0000-0002-4198-9279"]},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sourangshu Ghosh","raw_affiliation_strings":["Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India"],"raw_orcid":"https://orcid.org/0000-0002-4198-9279","affiliations":[{"raw_affiliation_string":"Department of Civil Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India","institution_ids":["https://openalex.org/I145894827"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072066459","display_name":"Adrian Abold","orcid":"https://orcid.org/0000-0002-1309-6254","observed_orcids":["https://orcid.org/0000-0002-1309-6254"]},"institutions":[{"id":"https://openalex.org/I181369854","display_name":"Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg","ror":"https://ror.org/00f7hpc57","country_code":"DE","type":"education","lineage":["https://openalex.org/I181369854"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Adrian Abold","raw_affiliation_strings":["Department of EEI, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403 Nuremberg, Germany"],"raw_orcid":"https://orcid.org/0000-0002-1309-6254","affiliations":[{"raw_affiliation_string":"Department of EEI, Friedrich-Alexander-Universit\u00e4t Erlangen-N\u00fcrnberg, Lange Gasse 20, 90403 Nuremberg, Germany","institution_ids":["https://openalex.org/I181369854"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040738895","display_name":"Alexander Rahn","orcid":"https://orcid.org/0000-0003-1691-4790","observed_orcids":["https://orcid.org/0000-0003-1691-4790"]},"institutions":[{"id":"https://openalex.org/I94626330","display_name":"University of Bamberg","ror":"https://ror.org/01c1w6d29","country_code":"DE","type":"education","lineage":["https://openalex.org/I94626330"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Alexander Rahn","raw_affiliation_strings":["Faculty of Information Systems and Applied Computer Sciences (WIAI), University of Bamberg, Kapuzinerstra\u00dfe 16, 96047 Bamberg, Germany"],"raw_orcid":"https://orcid.org/0000-0003-1691-4790","affiliations":[{"raw_affiliation_string":"Faculty of Information Systems and Applied Computer Sciences (WIAI), University of Bamberg, Kapuzinerstra\u00dfe 16, 96047 Bamberg, Germany","institution_ids":["https://openalex.org/I94626330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038896460","display_name":"Eldar Sultanow","orcid":"https://orcid.org/0000-0001-5257-2236","observed_orcids":["https://orcid.org/0000-0001-5257-2236"]},"institutions":[{"id":"https://openalex.org/I176453806","display_name":"University of Potsdam","ror":"https://ror.org/03bnmw459","country_code":"DE","type":"education","lineage":["https://openalex.org/I176453806"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Eldar Sultanow","raw_affiliation_strings":["Capgemini, Bahnhofstra\u00dfe 30, 90402 Nuremberg, Germany","Chair of Business Informatics, Processes and Systems, Potsdam University, Karl-Marx Stra\u00dfe 67, 14482 Potsdam, Germany"],"raw_orcid":"https://orcid.org/0000-0001-5257-2236","affiliations":[{"raw_affiliation_string":"Capgemini, Bahnhofstra\u00dfe 30, 90402 Nuremberg, Germany","institution_ids":[]},{"raw_affiliation_string":"Chair of Business Informatics, Processes and Systems, Potsdam University, Karl-Marx Stra\u00dfe 67, 14482 Potsdam, Germany","institution_ids":["https://openalex.org/I176453806"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5038896460"],"corresponding_institution_ids":["https://openalex.org/I176453806"],"apc_list":{"value":1000,"currency":"CHF","value_usd":1047},"apc_paid":{"value":1000,"currency":"CHF","value_usd":1047},"fwci":0.241,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.47210623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":96},"biblio":{"volume":"2","issue":"1","first_page":"104","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.2791000008583069,"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":0.2791000008583069,"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/T11166","display_name":"Analytic Number Theory Research","score":0.17790000140666962,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.13590000569820404,"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/hamming-weight","display_name":"Hamming weight","score":0.875},{"id":"https://openalex.org/keywords/divisibility","display_name":"divisibility","score":0.7940000295639038},{"id":"https://openalex.org/keywords/bit-length","display_name":"bit length","score":0.7049999833106995},{"id":"https://openalex.org/keywords/binary-numbers","display_name":"binary numbers","score":0.4830000102519989},{"id":"https://openalex.org/keywords/cycles","display_name":"cycles","score":0.3840000033378601}],"concepts":[{"id":"https://openalex.org/C9991821","wikidata":"https://www.wikidata.org/wiki/Q858520","display_name":"Divisibility rule","level":2,"score":0.9474083185195923},{"id":"https://openalex.org/C63361517","wikidata":"https://www.wikidata.org/wiki/Q5645805","display_name":"Hamming weight","level":5,"score":0.7703223824501038},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.741082489490509},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.637377142906189},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6174402832984924},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5917009115219116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5821117758750916},{"id":"https://openalex.org/C74050887","wikidata":"https://www.wikidata.org/wiki/Q848368","display_name":"Rotation (mathematics)","level":2,"score":0.5541955232620239},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4456164836883545},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.378013014793396},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.26510384678840637},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18594792485237122},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1642756462097168},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10605579614639282},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.0},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/appliedmath2010005","doi":"https://doi.org/10.3390/appliedmath2010005","is_oa":true,"landing_page_url":"https://doi.org/10.3390/appliedmath2010005","pdf_url":"https://www.mdpi.com/2673-9909/2/1/5/pdf?version=1644831784","source":{"id":"https://openalex.org/S4210196797","display_name":"AppliedMath","issn_l":"2673-9909","issn":["2673-9909"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AppliedMath","raw_type":"journal-article"},{"id":"pmh:oai:ub.uni-erlangen.de-opus:20628","doi":null,"is_oa":true,"landing_page_url":"https://opus4.kobv.de/opus4-fau/files/20628/appliedmath-02-00005-v2.pdf","pdf_url":"https://opus4.kobv.de/opus4-fau/files/20628/appliedmath-02-00005-v2.pdf","source":{"id":"https://openalex.org/S4306401636","display_name":"OPUS Repository (Kooperativer Bibliotheksverbund Berlin-Brandenburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/appliedmath2010005","doi":"https://doi.org/10.3390/appliedmath2010005","is_oa":true,"landing_page_url":"https://doi.org/10.3390/appliedmath2010005","pdf_url":"https://www.mdpi.com/2673-9909/2/1/5/pdf?version=1644831784","source":{"id":"https://openalex.org/S4210196797","display_name":"AppliedMath","issn_l":"2673-9909","issn":["2673-9909"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","norway-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"AppliedMath","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4210697516.pdf","grobid_xml":"https://content.openalex.org/works/W4210697516.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1544769168","https://openalex.org/W1723921989","https://openalex.org/W2005403482","https://openalex.org/W2593961314","https://openalex.org/W3080858956","https://openalex.org/W3156329559","https://openalex.org/W4235048180","https://openalex.org/W4238159413","https://openalex.org/W6651791023","https://openalex.org/W6674395678","https://openalex.org/W6816434393"],"related_works":["https://openalex.org/W2008960744","https://openalex.org/W2105471374","https://openalex.org/W2963549154","https://openalex.org/W2158117886","https://openalex.org/W1987803429","https://openalex.org/W1582340598","https://openalex.org/W2152162311","https://openalex.org/W1530654122","https://openalex.org/W2182731056","https://openalex.org/W3013281356"],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,14,25,31,38,45,56,61,67,70,79,84],"behavior":[4],"of":[5,16,33,41,47,73],"rotating":[6],"binaries.":[7],"A":[8],"rotation":[9],"by":[10],"r":[11,53],"digits":[12],"to":[13],"left":[15],"a":[17],"binary":[18,74],"number":[19,46],"B":[20,34],"exhibits":[21],"in":[22,49],"particular":[23],"cases":[24],"divisibility":[26,86,98],"l\u2223N1(B)\u00b7r+1,":[27],"where":[28],"l":[29],"is":[30,37,44,54,87],"bit-length":[32],"and":[35,69,93],"N1(B)":[36],"Hamming":[39,71],"weight":[40,72],"B,":[42],"that":[43,96],"ones":[48],"B.":[50],"The":[51],"integer":[52],"called":[55],"left-rotational":[57],"distance.":[58],"We":[59,89],"investigate":[60],"connection":[62],"between":[63],"this":[64,97],"rotational":[65],"distance,":[66],"length,":[68],"numbers.":[75],"Moreover,":[76],"we":[77],"follow":[78],"question":[80],"under":[81],"which":[82],"circumstances":[83],"above-mentioned":[85],"true.":[88],"have":[90],"found":[91],"out":[92],"will":[94],"demonstrate":[95],"occurs":[99],"for":[100],"kn+c":[101],"cycles.":[102]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2022-02-08T00:00:00"}
