{"id":"https://openalex.org/W2113028625","doi":"https://doi.org/10.1109/tc.2003.1244937","title":"Constructing composite field representations for efficient conversion","display_name":"Constructing composite field representations for efficient conversion","publication_year":2003,"publication_date":"2003-11-01","ids":{"openalex":"https://openalex.org/W2113028625","doi":"https://doi.org/10.1109/tc.2003.1244937","mag":"2113028625"},"language":"en","primary_location":{"id":"doi:10.1109/tc.2003.1244937","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2003.1244937","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/A5066592325","display_name":"Berk Sunar","orcid":"https://orcid.org/0000-0001-5404-5368"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"B. Sunar","raw_affiliation_strings":["Worcester Polytechnic Institute, Worcester, MA, USA","Worcester Polytech. Inst., MA, USA"],"affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute, Worcester, MA, USA","institution_ids":["https://openalex.org/I107077323"]},{"raw_affiliation_string":"Worcester Polytech. Inst., MA, USA","institution_ids":["https://openalex.org/I107077323"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064835031","display_name":"Erkay Sava\u015f","orcid":"https://orcid.org/0000-0002-4869-5556"},"institutions":[{"id":"https://openalex.org/I134235054","display_name":"Sabanc\u0131 \u00dcniversitesi","ror":"https://ror.org/049asqa32","country_code":"TR","type":"education","lineage":["https://openalex.org/I134235054"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"E. Savas","raw_affiliation_strings":["Faculty of Engineering and Natural Science, Sabanci University, Istanbul, Turkey",", Faculty of Engineering and Natural Science, Sabanci University, Istanbul, Turkey"],"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Natural Science, Sabanci University, Istanbul, Turkey","institution_ids":["https://openalex.org/I134235054"]},{"raw_affiliation_string":", Faculty of Engineering and Natural Science, Sabanci University, Istanbul, Turkey","institution_ids":["https://openalex.org/I134235054"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018100877","display_name":"\u00c7etin Kaya Ko\u00e7","orcid":"https://orcid.org/0000-0002-2572-9565"},"institutions":[{"id":"https://openalex.org/I131249849","display_name":"Oregon State University","ror":"https://ror.org/00ysfqy60","country_code":"US","type":"education","lineage":["https://openalex.org/I131249849"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C.K. Koc","raw_affiliation_strings":["Electrical and Computer Engineering Department, Oregon State University, Corvallis, OR, USA","[Electrical and Computer Engineering Department, Oregon State University, Corvallis, OR, USA]"],"affiliations":[{"raw_affiliation_string":"Electrical and Computer Engineering Department, Oregon State University, Corvallis, OR, USA","institution_ids":["https://openalex.org/I131249849"]},{"raw_affiliation_string":"[Electrical and Computer Engineering Department, Oregon State University, Corvallis, OR, USA]","institution_ids":["https://openalex.org/I131249849"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066592325"],"corresponding_institution_ids":["https://openalex.org/I107077323"],"apc_list":null,"apc_paid":null,"fwci":6.3915,"has_fulltext":false,"cited_by_count":38,"citation_normalized_percentile":{"value":0.96352041,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"52","issue":"11","first_page":"1391","last_page":"1398"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9987999796867371,"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":0.9987999796867371,"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":0.996399998664856,"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":0.9764000177383423,"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/field","display_name":"Field (mathematics)","score":0.7038793563842773},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6802645325660706},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6407216787338257},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5805069208145142},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5737553834915161},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5721263885498047},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.5666162967681885},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5255888104438782},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5206570029258728},{"id":"https://openalex.org/keywords/composite-number","display_name":"Composite number","score":0.5175527930259705},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5002577304840088},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.45675310492515564},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3947340250015259},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3761367201805115},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33023303747177124},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29626479744911194},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2859744727611542},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2590180039405823},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.24035608768463135},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.21410465240478516},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1601335108280182},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09753692150115967},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.07451304793357849}],"concepts":[{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.7038793563842773},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6802645325660706},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6407216787338257},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5805069208145142},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5737553834915161},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5721263885498047},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.5666162967681885},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5255888104438782},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5206570029258728},{"id":"https://openalex.org/C104779481","wikidata":"https://www.wikidata.org/wiki/Q50707","display_name":"Composite number","level":2,"score":0.5175527930259705},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5002577304840088},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.45675310492515564},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3947340250015259},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3761367201805115},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33023303747177124},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29626479744911194},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2859744727611542},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2590180039405823},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.24035608768463135},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.21410465240478516},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1601335108280182},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09753692150115967},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.07451304793357849},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tc.2003.1244937","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.2003.1244937","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"},{"id":"pmh:oai:research.sabanciuniv.edu:438","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402254","display_name":"Sabanci University","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I134235054","host_organization_name":"Sabanc\u0131 \u00dcniversitesi","host_organization_lineage":["https://openalex.org/I134235054"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.383.1710","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.383.1710","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.crypto.wpi.edu/Publications/Documents/SunarSavasKocTC2003.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5,"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":18,"referenced_works":["https://openalex.org/W1515926918","https://openalex.org/W1520091057","https://openalex.org/W1529013801","https://openalex.org/W1529417005","https://openalex.org/W1549861330","https://openalex.org/W1559182355","https://openalex.org/W1560768562","https://openalex.org/W1569612250","https://openalex.org/W2127752881","https://openalex.org/W2130623996","https://openalex.org/W2144129711","https://openalex.org/W2154260654","https://openalex.org/W2154419929","https://openalex.org/W2158119726","https://openalex.org/W3030671011","https://openalex.org/W4285719527","https://openalex.org/W6778341561","https://openalex.org/W7018817413"],"related_works":["https://openalex.org/W2075768550","https://openalex.org/W3022218857","https://openalex.org/W2369178846","https://openalex.org/W2082716031","https://openalex.org/W3161230432","https://openalex.org/W2370289839","https://openalex.org/W2933494595","https://openalex.org/W2548984902","https://openalex.org/W1955455432","https://openalex.org/W4299961354"],"abstract_inverted_index":{"We":[0,17],"describe":[1],"a":[2,7,12],"method":[3],"of":[4,6,22,28,32,70,78,84,109],"construction":[5,73,83],"composite":[8,49,85,104],"field":[9,15,35,50,58,112],"representation":[10],"from":[11,54],"given":[13],"binary":[14,56,102],"representation.":[16],"derive":[18],"the":[19,30,33,40,44,48,55,61,71,76,82,101,107,110,117],"conversion":[20,98],"(change":[21],"basis)":[23],"matrix.":[24],"The":[25],"special":[26,88],"case":[27],"when":[29,106],"degree":[31,108],"ground":[34,62,111],"is":[36,64,113],"relatively":[37,114],"prime":[38,57,115],"to":[39,116],"extension":[41,118],"degree,":[42],"where":[43],"irreducible":[45,89],"polynomial":[46],"generating":[47],"has":[51],"its":[52],"coefficients":[53],"rather":[59],"than":[60],"field,":[63],"also":[65,92],"treated.":[66],"Furthermore,":[67],"certain":[68],"generalizations":[69],"proposed":[72],"method,":[74],"e.g.,":[75],"use":[77],"nonprimitive":[79],"elements":[80],"and":[81,103],"fields":[86,105],"with":[87],"polynomials,":[90],"are":[91],"discussed.":[93],"Finally,":[94],"we":[95],"give":[96],"storage-efficient":[97],"algorithms":[99],"between":[100],"degree.":[119]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
