{"id":"https://openalex.org/W2466335964","doi":"https://doi.org/10.1142/s0129054116500106","title":"GF(2<sup><i>n</i></sup>) Redundant Representation Using Matrix Embedding for Irreducible Trinomials","display_name":"GF(2<sup><i>n</i></sup>) Redundant Representation Using Matrix Embedding for Irreducible Trinomials","publication_year":2016,"publication_date":"2016-06-01","ids":{"openalex":"https://openalex.org/W2466335964","doi":"https://doi.org/10.1142/s0129054116500106","mag":"2466335964"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054116500106","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054116500106","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5078403031","display_name":"Yongjia Wang","orcid":"https://orcid.org/0000-0003-2506-0010"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongjia Wang","raw_affiliation_strings":["School of Software, Tsinghua University, Beijing, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Software, Tsinghua University, Beijing, P. R. China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057936279","display_name":"Xi Xiong","orcid":"https://orcid.org/0000-0002-3123-4200"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xi Xiong","raw_affiliation_strings":["School of Software, Tsinghua University, Beijing, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Software, Tsinghua University, Beijing, P. R. China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013230768","display_name":"Haining Fan","orcid":"https://orcid.org/0000-0001-7791-5725"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haining Fan","raw_affiliation_strings":["School of Software, Tsinghua University, Beijing, P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Software, Tsinghua University, Beijing, P. R. China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078403031"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07462997,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"27","issue":"04","first_page":"463","last_page":"478"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9991999864578247,"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/T11130","display_name":"Coding theory and cryptography","score":0.9973999857902527,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9941999912261963,"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/trinomial","display_name":"Trinomial","score":0.897433340549469},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7635936141014099},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.7500090599060059},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.6363442540168762},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5695865750312805},{"id":"https://openalex.org/keywords/matrix-multiplication","display_name":"Matrix multiplication","score":0.519180417060852},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5188001990318298},{"id":"https://openalex.org/keywords/gf","display_name":"GF(2)","score":0.51655113697052},{"id":"https://openalex.org/keywords/fast-fourier-transform","display_name":"Fast Fourier transform","score":0.5125555992126465},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.512008011341095},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43795400857925415},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.42618048191070557},{"id":"https://openalex.org/keywords/embedding","display_name":"Embedding","score":0.4228115975856781},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.41341447830200195},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.26442015171051025},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.23368722200393677},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20138758420944214},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12872862815856934}],"concepts":[{"id":"https://openalex.org/C6791720","wikidata":"https://www.wikidata.org/wiki/Q1670509","display_name":"Trinomial","level":2,"score":0.897433340549469},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7635936141014099},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.7500090599060059},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.6363442540168762},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5695865750312805},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.519180417060852},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5188001990318298},{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.51655113697052},{"id":"https://openalex.org/C75172450","wikidata":"https://www.wikidata.org/wiki/Q623950","display_name":"Fast Fourier transform","level":2,"score":0.5125555992126465},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.512008011341095},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43795400857925415},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.42618048191070557},{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.4228115975856781},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.41341447830200195},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.26442015171051025},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.23368722200393677},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20138758420944214},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12872862815856934},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0129054116500106","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054116500106","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W181760484","https://openalex.org/W1492069598","https://openalex.org/W1969341770","https://openalex.org/W1995503477","https://openalex.org/W2006550573","https://openalex.org/W2032523493","https://openalex.org/W2051495459","https://openalex.org/W2057951266","https://openalex.org/W2060746229","https://openalex.org/W2105427204","https://openalex.org/W2114625600","https://openalex.org/W2127977400","https://openalex.org/W2139916957","https://openalex.org/W2145823187","https://openalex.org/W2148386700","https://openalex.org/W2150782829","https://openalex.org/W2167456209","https://openalex.org/W2242376712","https://openalex.org/W4233307210","https://openalex.org/W4388283664"],"related_works":["https://openalex.org/W3177828492","https://openalex.org/W2034415022","https://openalex.org/W2149698301","https://openalex.org/W4388372565","https://openalex.org/W2286689764","https://openalex.org/W63525287","https://openalex.org/W4388372654","https://openalex.org/W2026406497","https://openalex.org/W2105266774","https://openalex.org/W1444802581"],"abstract_inverted_index":{"By":[0],"embedding":[1],"a":[2,11,28,38,58],"Toeplitz":[3],"matrix-vector":[4],"product":[5],"(MVP)":[6],"of":[7,14,51,100],"dimension":[8,15],"n":[9,30,104],"into":[10],"circulant":[12],"MVP":[13],"[Formula:":[16,68],"see":[17,69],"text],":[18],"where":[19],"\u03b4":[20,52],"can":[21,71],"be":[22,72],"any":[23],"nonnegative":[24],"integer,":[25],"we":[26],"present":[27],"GF(2":[29,103],")":[31,105],"multiplication":[32,64,85],"algorithm.":[33],"This":[34],"algorithm":[35],"leads":[36],"to":[37,56,115],"new":[39],"redundant":[40,89,106],"representation,":[41],"and":[42,108],"it":[43,54],"has":[44],"two":[45],"merits:":[46],"(1)":[47],"The":[48,88],"flexible":[49],"choices":[50],"make":[53],"possible":[55],"select":[57],"proper":[59],"N":[60],"such":[61],"that":[62],"the":[63,80],"operation":[65],"in":[66,109],"ring":[67],"text]":[70],"performed":[73],"using":[74],"some":[75],"asymptotically":[76],"faster":[77],"algorithms,":[78],"e.g.":[79],"Fast":[81],"Fourier":[82],"Transformation":[83],"(FFT)-based":[84],"algorithm;":[86],"(2)":[87],"degrees,":[90],"which":[91],"are":[92,96,112],"defined":[93],"as":[94],"N/n,":[95],"smaller":[97],"than":[98],"those":[99],"most":[101],"previous":[102],"representations,":[107],"fact":[110],"they":[111],"approximately":[113],"equal":[114],"2":[116],"for":[117],"all":[118],"applicable":[119],"cases.":[120]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
