{"id":"https://openalex.org/W2114169681","doi":"https://doi.org/10.1109/ismvl.2003.1201424","title":"Family of fast transforms over GF(3) logic","display_name":"Family of fast transforms over GF(3) logic","publication_year":2004,"publication_date":"2004-06-22","ids":{"openalex":"https://openalex.org/W2114169681","doi":"https://doi.org/10.1109/ismvl.2003.1201424","mag":"2114169681"},"language":"en","primary_location":{"id":"doi:10.1109/ismvl.2003.1201424","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ismvl.2003.1201424","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.","raw_type":"proceedings-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/A5016478346","display_name":"B.J. Falkowski","orcid":null},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"B.J. Falkowski","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101780628","display_name":"Cheng Fu","orcid":"https://orcid.org/0000-0002-1280-2057"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Cheng Fu","raw_affiliation_strings":["School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, , Singapore","institution_ids":["https://openalex.org/I172675005"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I172675005"],"apc_list":null,"apc_paid":null,"fwci":5.0379,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.95193191,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"323","last_page":"328"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.25940001010894775,"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":0.25940001010894775,"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":0.1624000072479248,"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"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.1589999943971634,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.588515043258667},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5767461657524109},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5383708477020264},{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.48107385635375977},{"id":"https://openalex.org/keywords/gf","display_name":"GF(2)","score":0.46306318044662476},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.45559999346733093},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.44913071393966675},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39464378356933594},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3920135796070099},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3656274676322937},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.31863194704055786},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2942730188369751},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1277790367603302}],"concepts":[{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.588515043258667},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5767461657524109},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5383708477020264},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.48107385635375977},{"id":"https://openalex.org/C156350748","wikidata":"https://www.wikidata.org/wiki/Q5513324","display_name":"GF(2)","level":3,"score":0.46306318044662476},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45559999346733093},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.44913071393966675},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39464378356933594},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3920135796070099},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3656274676322937},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.31863194704055786},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2942730188369751},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1277790367603302},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ismvl.2003.1201424","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ismvl.2003.1201424","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"33rd International Symposium on Multiple-Valued Logic, 2003. Proceedings.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1481714151","https://openalex.org/W1498138768","https://openalex.org/W1975442699","https://openalex.org/W2113597213","https://openalex.org/W2116013656","https://openalex.org/W2119617508","https://openalex.org/W2163000354","https://openalex.org/W4248793972"],"related_works":["https://openalex.org/W1825396486","https://openalex.org/W843373033","https://openalex.org/W2587136861","https://openalex.org/W2127172196","https://openalex.org/W793948417","https://openalex.org/W2390270234","https://openalex.org/W1976396586","https://openalex.org/W1528972180","https://openalex.org/W2125381587","https://openalex.org/W2135192133"],"abstract_inverted_index":{"New":[0],"classes":[1,50],"of":[2,51],"recursive":[3,16],"transforms":[4,27,40,54],"over":[5],"GF(3)":[6],"have":[7],"been":[8],"introduced":[9,52],"here.":[10],"They":[11],"are":[12,55],"based":[13],"on":[14],"simple":[15],"equations":[17],"what":[18],"allows":[19],"to":[20],"obtain":[21],"corresponding":[22],"fast":[23],"forward":[24],"and":[25,28,43],"inverse":[26],"very":[29],"regular":[30],"butterfly":[31],"diagrams.":[32],"The":[33,46],"classification":[34],"is":[35],"further":[36],"extended":[37],"into":[38],"various":[39,49],"with":[41],"horizontal":[42],"vertical":[44],"permutations.":[45],"relations":[47],"between":[48],"ternary":[53],"also":[56],"discussed.":[57]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
