{"id":"https://openalex.org/W3117553605","doi":"https://doi.org/10.23919/eusipco47968.2020.9287751","title":"Arbitrary Length Reducible and Irreducible Perfect Gaussian Integer Sequences with A Pre-Given Gaussian Integer","display_name":"Arbitrary Length Reducible and Irreducible Perfect Gaussian Integer Sequences with A Pre-Given Gaussian Integer","publication_year":2020,"publication_date":"2020-12-18","ids":{"openalex":"https://openalex.org/W3117553605","doi":"https://doi.org/10.23919/eusipco47968.2020.9287751","mag":"3117553605"},"language":"en","primary_location":{"id":"doi:10.23919/eusipco47968.2020.9287751","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco47968.2020.9287751","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 28th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5085279585","display_name":"Soo\u2010Chang Pei","orcid":"https://orcid.org/0000-0003-2448-4196"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Soo-Chang Pei","raw_affiliation_strings":["National Taiwan University, Taipei, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan University, Taipei, Taiwan, R.O.C","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054825387","display_name":"Kuo-Wei Chang","orcid":"https://orcid.org/0000-0002-5987-6862"},"institutions":[{"id":"https://openalex.org/I92172085","display_name":"Chunghwa Telecom (Taiwan)","ror":"https://ror.org/04f786589","country_code":"TW","type":"company","lineage":["https://openalex.org/I92172085"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kuo-Wei Chang","raw_affiliation_strings":["Telecommunication Laboratories, Chunghwa Telecom, Taoyuang, Taiwan, R.O.C"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Telecommunication Laboratories, Chunghwa Telecom, Taoyuang, Taiwan, R.O.C","institution_ids":["https://openalex.org/I92172085"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.17784026,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2274","last_page":"2278"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9995999932289124,"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"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9983999729156494,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/gaussian-integer","display_name":"Gaussian integer","score":0.8089662194252014},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.8019261360168457},{"id":"https://openalex.org/keywords/ramanujans-sum","display_name":"Ramanujan's sum","score":0.7524847984313965},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6853940486907959},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5769940614700317},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.5121734142303467},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4592016637325287},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.44949057698249817},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4189067482948303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3999940752983093},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20497086644172668},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08271467685699463},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.055223286151885986}],"concepts":[{"id":"https://openalex.org/C120561534","wikidata":"https://www.wikidata.org/wiki/Q724975","display_name":"Gaussian integer","level":2,"score":0.8089662194252014},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.8019261360168457},{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.7524847984313965},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6853940486907959},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5769940614700317},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.5121734142303467},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4592016637325287},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.44949057698249817},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4189067482948303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3999940752983093},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20497086644172668},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08271467685699463},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.055223286151885986},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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":1,"locations":[{"id":"doi:10.23919/eusipco47968.2020.9287751","is_oa":false,"landing_page_url":"https://doi.org/10.23919/eusipco47968.2020.9287751","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 28th European Signal Processing Conference (EUSIPCO)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5199999809265137,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1505761511","https://openalex.org/W1806232464","https://openalex.org/W1829788117","https://openalex.org/W1977449481","https://openalex.org/W2000329328","https://openalex.org/W2001646739","https://openalex.org/W2011059145","https://openalex.org/W2027669898","https://openalex.org/W2033699179","https://openalex.org/W2044842474","https://openalex.org/W2081825044","https://openalex.org/W2088866385","https://openalex.org/W2114788954","https://openalex.org/W2121743251","https://openalex.org/W2124526648","https://openalex.org/W2136017419","https://openalex.org/W2243404481","https://openalex.org/W2597177126","https://openalex.org/W2626357105","https://openalex.org/W2903081438","https://openalex.org/W2948354211","https://openalex.org/W2948981572"],"related_works":["https://openalex.org/W3096644734","https://openalex.org/W2516138189","https://openalex.org/W4280608413","https://openalex.org/W2369409824","https://openalex.org/W2971248009","https://openalex.org/W2414755644","https://openalex.org/W2964093280","https://openalex.org/W2077158246","https://openalex.org/W4299834941","https://openalex.org/W3106993171"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"will":[4,32],"discuss":[5,34],"two":[6],"construction":[7],"schemes":[8],"on":[9],"arbitrary":[10],"length":[11,59],"perfect":[12],"Gaussian":[13],"integer":[14],"sequence":[15],"(PGIS)":[16],"with":[17],"a":[18],"pre-given":[19],"constant.":[20],"The":[21],"first":[22],"scheme":[23],"uses":[24],"geometric":[25],"series,":[26],"which":[27],"brings":[28],"reducible":[29],"PGIS.":[30],"We":[31],"also":[33],"the":[35,50],"irreducible":[36],"case":[37],"and":[38],"find":[39],"an":[40],"easy":[41],"way":[42],"to":[43],"obtain":[44],"PGIS":[45],"for":[46,56],"even":[47],"length.":[48],"Moreover,":[49],"same":[51],"concept":[52],"can":[53],"be":[54],"applied":[55],"some":[57],"odd":[58],"N":[60],"=":[61],"3p":[62],"by":[63],"using":[64],"Ramanujan's":[65],"Sum.":[66],"Concrete":[67],"examples":[68],"are":[69],"provided.":[70]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
