{"id":"https://openalex.org/W2018209517","doi":"https://doi.org/10.1109/tc.2003.1244950","title":"New systolic architectures for inversion and division in GF(2/sup m/)","display_name":"New systolic architectures for inversion and division in GF(2/sup m/)","publication_year":2003,"publication_date":"2003-11-01","ids":{"openalex":"https://openalex.org/W2018209517","doi":"https://doi.org/10.1109/tc.2003.1244950","mag":"2018209517"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2003.1244950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2003.1244950","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"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 Computers","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/A5027079185","display_name":"Zhiyuan Yan","orcid":"https://orcid.org/0000-0002-7114-6758"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhiyuan Yan","raw_affiliation_strings":["Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana-Champaign, IL, USA"],"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana-Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070800719","display_name":"D.V. Sarwate","orcid":null},"institutions":[{"id":"https://openalex.org/I183874917","display_name":"Urbana University","ror":"https://ror.org/04kp3hw27","country_code":"US","type":"education","lineage":["https://openalex.org/I183874917"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D.V. Sarwate","raw_affiliation_strings":["Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana-Champaign, IL, USA","Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA"],"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory and the Department of Electrical and Computer Engineering, University of Illinois, Urbana-Champaign, Urbana-Champaign, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA","institution_ids":["https://openalex.org/I183874917"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5027079185"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":4.5693,"has_fulltext":false,"cited_by_count":60,"citation_normalized_percentile":{"value":0.94622639,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"52","issue":"11","first_page":"1515","last_page":"1520"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987000226974487,"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/T12162","display_name":"Cellular Automata and Applications","score":0.996399998664856,"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/adder","display_name":"Adder","score":0.6876639723777771},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5911392569541931},{"id":"https://openalex.org/keywords/division","display_name":"Division (mathematics)","score":0.5852655172348022},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5180913805961609},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4918051064014435},{"id":"https://openalex.org/keywords/systolic-array","display_name":"Systolic array","score":0.4619240164756775},{"id":"https://openalex.org/keywords/very-large-scale-integration","display_name":"Very-large-scale integration","score":0.41095829010009766},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3768327236175537},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.36207684874534607},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33836957812309265},{"id":"https://openalex.org/keywords/embedded-system","display_name":"Embedded system","score":0.10452482104301453},{"id":"https://openalex.org/keywords/telecommunications","display_name":"Telecommunications","score":0.08707565069198608}],"concepts":[{"id":"https://openalex.org/C164620267","wikidata":"https://www.wikidata.org/wiki/Q376953","display_name":"Adder","level":3,"score":0.6876639723777771},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5911392569541931},{"id":"https://openalex.org/C60798267","wikidata":"https://www.wikidata.org/wiki/Q1226939","display_name":"Division (mathematics)","level":2,"score":0.5852655172348022},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5180913805961609},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4918051064014435},{"id":"https://openalex.org/C150741067","wikidata":"https://www.wikidata.org/wiki/Q2377218","display_name":"Systolic array","level":3,"score":0.4619240164756775},{"id":"https://openalex.org/C14580979","wikidata":"https://www.wikidata.org/wiki/Q876049","display_name":"Very-large-scale integration","level":2,"score":0.41095829010009766},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3768327236175537},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.36207684874534607},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33836957812309265},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.10452482104301453},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.08707565069198608},{"id":"https://openalex.org/C82876162","wikidata":"https://www.wikidata.org/wiki/Q17096504","display_name":"Latency (audio)","level":2,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.2003.1244950","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2003.1244950","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","1557-9956","2326-3814"],"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 Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W3639359","https://openalex.org/W124596592","https://openalex.org/W1533899290","https://openalex.org/W1547846260","https://openalex.org/W1582639393","https://openalex.org/W1593683169","https://openalex.org/W1594652978","https://openalex.org/W1607201894","https://openalex.org/W1784953981","https://openalex.org/W1882297107","https://openalex.org/W1906704443","https://openalex.org/W1929014668","https://openalex.org/W1986771232","https://openalex.org/W1989675557","https://openalex.org/W1991816802","https://openalex.org/W2017369466","https://openalex.org/W2023845097","https://openalex.org/W2075054028","https://openalex.org/W2075850503","https://openalex.org/W2082964102","https://openalex.org/W2099711671","https://openalex.org/W2100556391","https://openalex.org/W2102009882","https://openalex.org/W2113678244","https://openalex.org/W2113682558","https://openalex.org/W2132450208","https://openalex.org/W2149181525","https://openalex.org/W2154123414","https://openalex.org/W2156186849","https://openalex.org/W2165293272","https://openalex.org/W2503268713","https://openalex.org/W3136905136","https://openalex.org/W6600159346","https://openalex.org/W6636297571","https://openalex.org/W6640585031"],"related_works":["https://openalex.org/W4390550886","https://openalex.org/W3217463396","https://openalex.org/W2790557758","https://openalex.org/W2516396101","https://openalex.org/W3204929712","https://openalex.org/W2015155483","https://openalex.org/W2038682752","https://openalex.org/W2142131433","https://openalex.org/W2739720767","https://openalex.org/W2105613219"],"abstract_inverted_index":{"We":[0],"present":[1],"two":[2,125],"systolic":[3],"architectures":[4,20,60],"for":[5,85,90],"inversion":[6,86],"and":[7,38,46,80],"division":[8],"in":[9,28,53],"GF(2/sup":[10],"m/)":[11],"based":[12],"on":[13],"a":[14],"modified":[15],"extended":[16],"Euclidean":[17],"algorithm.":[18],"Our":[19],"are":[21,66,83],"similar":[22,56],"to":[23,55,76,123],"those":[24],"proposed":[25],"by":[26],"others":[27],"that":[29,65,70,82],"they":[30],"consist":[31],"of":[32,35],"two-dimensional":[33],"arrays":[34],"computing":[36,116],"cells":[37,40],"control":[39,104,121],"with":[41],"only":[42,77],"local":[43],"intercell":[44],"connections":[45],"have":[47,61],"O(m/sup":[48],"2/)":[49],"area-time":[50],"product.":[51],"However,":[52],"comparison":[54],"architectures,":[57],"both":[58],"our":[59],"critical":[62],"path":[63],"delays":[64],"smaller,":[67],"gate":[68],"counts":[69],"range":[71],"from":[72],"being":[73],"considerably":[74],"smaller":[75],"slightly":[78],"larger,":[79],"latencies":[81],"identical":[84],"but":[87],"somewhat":[88],"larger":[89],"division.":[91],"One":[92],"architecture":[93,109],"uses":[94],"an":[95,98],"adder":[96],"or":[97],"(m+l)-bit":[99],"ring":[100,112],"counter":[101],"inside":[102],"each":[103,120],"cell,":[105],"while":[106],"the":[107,111,115],"other":[108],"distributes":[110],"counters":[113],"into":[114],"cells,":[117],"thereby":[118],"reducing":[119],"cell":[122],"just":[124],"gates.":[126]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
