{"id":"https://openalex.org/W2249088385","doi":"https://doi.org/10.48550/arxiv.1504.01099","title":"CRT and Fixed Patterns in Combinatorial Sequences","display_name":"CRT and Fixed Patterns in Combinatorial Sequences","publication_year":2015,"publication_date":"2015-04-05","ids":{"openalex":"https://openalex.org/W2249088385","doi":"https://doi.org/10.48550/arxiv.1504.01099","mag":"2249088385"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1504.01099","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.01099","pdf_url":"https://arxiv.org/pdf/1504.01099","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1504.01099","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101636357","display_name":"Muhammad Asad Khan","orcid":"https://orcid.org/0000-0001-7963-6615","observed_orcids":["https://orcid.org/0000-0001-7963-6615"]},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khan, Muhammad Asad","raw_affiliation_strings":["National University of Sciences and Technology , Islamabad , Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Sciences and Technology , Islamabad , Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070545670","display_name":"Amir Ali Khan","orcid":"https://orcid.org/0000-0002-3309-9831","observed_orcids":["https://orcid.org/0000-0002-3309-9831"]},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Khan, Amir Ali","raw_affiliation_strings":["National University of Sciences and Technology , Islamabad , Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Sciences and Technology , Islamabad , Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073978672","display_name":"Fauzan Mirza","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Mirza, Fauzan","raw_affiliation_strings":["National University of Sciences and Technology , Islamabad , Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National University of Sciences and Technology , Islamabad , Pakistan","institution_ids":["https://openalex.org/I929597975"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I929597975"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9951000213623047,"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"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9951000213623047,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.00019999999494757503,"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/chinese-remainder-theorem","display_name":"Chinese remainder theorem","score":0.9639999866485596},{"id":"https://openalex.org/keywords/combinatorial-sequences","display_name":"combinatorial sequences","score":0.777999997138977},{"id":"https://openalex.org/keywords/linear-feedback-shift-registers","display_name":"linear feedback shift registers","score":0.8709999918937683},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.8019999861717224},{"id":"https://openalex.org/keywords/ring-structure","display_name":"ring structure","score":0.9169999957084656},{"id":"https://openalex.org/keywords/discrete-fourier-transform","display_name":"discrete Fourier transform","score":0.7210000157356262},{"id":"https://openalex.org/keywords/spectral-analysis","display_name":"spectral analysis","score":0.4350000023841858},{"id":"https://openalex.org/keywords/pseudorandom-sequence-generation","display_name":"pseudorandom sequence generation","score":0.6759999990463257}],"concepts":[{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7275380492210388},{"id":"https://openalex.org/C151635116","wikidata":"https://www.wikidata.org/wiki/Q193878","display_name":"Chinese remainder theorem","level":2,"score":0.7236014008522034},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6585993766784668},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6295976042747498},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6030465960502625},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.567051112651825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.48115289211273193},{"id":"https://openalex.org/C2779521423","wikidata":"https://www.wikidata.org/wiki/Q3855646","display_name":"Combinatorial method","level":2,"score":0.47194331884384155},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4653848707675934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42055243253707886},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4203988313674927},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.42024359107017517},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3937034606933594},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3414493501186371},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.2671812176704407},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2198936939239502},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16664773225784302},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07142984867095947},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"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}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:1504.01099","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.01099","pdf_url":"https://arxiv.org/pdf/1504.01099","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1504.01099","doi":"https://doi.org/10.48550/arxiv.1504.01099","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1504.01099","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1504.01099","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1504.01099","pdf_url":"https://arxiv.org/pdf/1504.01099","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2249088385.pdf","grobid_xml":"https://content.openalex.org/works/W2249088385.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W39299451","https://openalex.org/W1586944506","https://openalex.org/W1593683169","https://openalex.org/W1979198062","https://openalex.org/W2069448237","https://openalex.org/W2142469562","https://openalex.org/W2150852850","https://openalex.org/W2154123414","https://openalex.org/W2161517294","https://openalex.org/W4243205024"],"related_works":["https://openalex.org/W1571650854","https://openalex.org/W2991305869","https://openalex.org/W2003802110","https://openalex.org/W4415353380","https://openalex.org/W1571223621","https://openalex.org/W1590992221","https://openalex.org/W2187584121","https://openalex.org/W1498467039","https://openalex.org/W4254166039","https://openalex.org/W2118500484"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"new":[3],"context":[4],"of":[5,12,33,38,41,54,63,68,89,98],"Chinese":[6],"Remainder":[7],"Theorem":[8],"(CRT)":[9],"based":[10,65,70],"analysis":[11,67],"combinatorial":[13,71],"sequence":[14,72],"generators":[15,91],"has":[16],"been":[17],"presented.":[18],"CRT":[19,64],"is":[20,58,73,84,93],"exploited":[21],"to":[22,95],"establish":[23],"fixed":[24],"patterns":[25],"in":[26,45,76],"LFSR":[27,69],"sequences":[28],"and":[29,78,92],"underlying":[30],"cyclic":[31],"structures":[32],"finite":[34,47],"fields.":[35],"New":[36],"methodology":[37],"direct":[39],"computations":[40],"DFT":[42,51],"spectral":[43],"points":[44,53],"higher":[46],"fields":[48,57],"from":[49],"known":[50],"spectra":[52],"smaller":[55],"constituent":[56],"also":[59],"introduced.":[60],"Novel":[61],"approach":[62,83],"structural":[66],"given":[74],"both":[75],"time":[77],"frequency":[79],"domain.":[80],"The":[81],"proposed":[82],"demonstrated":[85],"on":[86],"some":[87],"examples":[88],"combiner":[90,99],"scalable":[94],"general":[96],"configuration":[97],"generators.":[100]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}