{"id":"https://openalex.org/W2343282431","doi":"https://doi.org/10.1109/iwsda.2015.7458407","title":"Multiplication in a Galois ring","display_name":"Multiplication in a Galois ring","publication_year":2015,"publication_date":"2015-09-01","ids":{"openalex":"https://openalex.org/W2343282431","doi":"https://doi.org/10.1109/iwsda.2015.7458407","mag":"2343282431"},"language":"en","primary_location":{"id":"doi:10.1109/iwsda.2015.7458407","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iwsda.2015.7458407","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 Seventh International Workshop on Signal Design and its Applications in Communications (IWSDA)","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/A5039513308","display_name":"Sedat Akleylek","orcid":"https://orcid.org/0000-0001-7005-6489"},"institutions":[{"id":"https://openalex.org/I227306068","display_name":"Ondokuz May\u0131s University","ror":"https://ror.org/028k5qw24","country_code":"TR","type":"education","lineage":["https://openalex.org/I227306068"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Sedat Akleyleky","raw_affiliation_strings":["Ondokuz Mayis Universitesi, Samsun, TR"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ondokuz Mayis Universitesi, Samsun, TR","institution_ids":["https://openalex.org/I227306068"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072676327","display_name":"Ferruh \u00d6zbudak","orcid":"https://orcid.org/0000-0002-1694-9283"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ferruh Ozbudak","raw_affiliation_strings":["Department of Mathematics and Institute of Applied Mathematics, METU, Ankara, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Institute of Applied Mathematics, METU, Ankara, Turkey","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"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":0.19005266,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"59","issue":null,"first_page":"28","last_page":"32"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"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":1.0,"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":0.9991000294685364,"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/T10849","display_name":"Finite Group Theory Research","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/multiplication","display_name":"Multiplication (music)","score":0.7685500383377075},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6950504779815674},{"id":"https://openalex.org/keywords/multiplication-algorithm","display_name":"Multiplication algorithm","score":0.6578434705734253},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.654604971408844},{"id":"https://openalex.org/keywords/normal-basis","display_name":"Normal basis","score":0.5680844783782959},{"id":"https://openalex.org/keywords/galois-theory","display_name":"Galois theory","score":0.5280685424804688},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.5072500109672546},{"id":"https://openalex.org/keywords/galois-module","display_name":"Galois module","score":0.4917927086353302},{"id":"https://openalex.org/keywords/galois-group","display_name":"Galois group","score":0.43680456280708313},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43197354674339294},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42934924364089966},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.39347925782203674},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3411129415035248},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2750694453716278},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.17606526613235474}],"concepts":[{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.7685500383377075},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6950504779815674},{"id":"https://openalex.org/C201290732","wikidata":"https://www.wikidata.org/wiki/Q130762","display_name":"Multiplication algorithm","level":3,"score":0.6578434705734253},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.654604971408844},{"id":"https://openalex.org/C205567592","wikidata":"https://www.wikidata.org/wiki/Q3527199","display_name":"Normal basis","level":3,"score":0.5680844783782959},{"id":"https://openalex.org/C94398972","wikidata":"https://www.wikidata.org/wiki/Q92552","display_name":"Galois theory","level":2,"score":0.5280685424804688},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.5072500109672546},{"id":"https://openalex.org/C145899342","wikidata":"https://www.wikidata.org/wiki/Q3427418","display_name":"Galois module","level":2,"score":0.4917927086353302},{"id":"https://openalex.org/C67536143","wikidata":"https://www.wikidata.org/wiki/Q730384","display_name":"Galois group","level":2,"score":0.43680456280708313},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43197354674339294},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42934924364089966},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.39347925782203674},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3411129415035248},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2750694453716278},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.17606526613235474},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/iwsda.2015.7458407","is_oa":false,"landing_page_url":"https://doi.org/10.1109/iwsda.2015.7458407","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 Seventh International Workshop on Signal Design and its Applications in Communications (IWSDA)","raw_type":"proceedings-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/W234037778","https://openalex.org/W597381772","https://openalex.org/W1487564550","https://openalex.org/W1509309609","https://openalex.org/W1773872090","https://openalex.org/W1976677460","https://openalex.org/W1980201978","https://openalex.org/W2011170492","https://openalex.org/W2017533742","https://openalex.org/W2038681062","https://openalex.org/W2048832337","https://openalex.org/W2096047691","https://openalex.org/W2100128294","https://openalex.org/W2125226017","https://openalex.org/W2137765248","https://openalex.org/W2150782829","https://openalex.org/W2167031391","https://openalex.org/W2168674495","https://openalex.org/W4229826396","https://openalex.org/W6684630281"],"related_works":["https://openalex.org/W2730690530","https://openalex.org/W2189024741","https://openalex.org/W2066449478","https://openalex.org/W1590581886","https://openalex.org/W4236770967","https://openalex.org/W4299357620","https://openalex.org/W1497806779","https://openalex.org/W2075372418","https://openalex.org/W2050642536","https://openalex.org/W2174459132"],"abstract_inverted_index":{"In":[0],"this":[1,63,91],"paper,":[2],"we":[3,65],"focus":[4],"on":[5],"the":[6,14,27,33,39,43,67,72,86,93,107],"efficient":[7],"multiplication":[8,30,41,50,68],"in":[9,42,56,106],"a":[10,20,47,53,98],"Galois":[11,34,44,80,108],"ring":[12,35,45],"of":[13,59,82,88],"size":[15],"4n,":[16],"where":[17],"n":[18],"is":[19,92],"positive":[21],"integer.":[22],"We":[23,37],"consider":[24],"to":[25,32,79,96,102],"adapt":[26],"finite":[28,57],"field":[29],"methods":[31],"multiplication.":[36],"give":[38],"polynomial":[40],"as":[46],"Toeplitz":[48],"matrix-vector":[49],"design":[51],"with":[52],"modification":[54],"used":[55],"fields":[58],"characteristic":[60],"two.":[61],"By":[62],"method,":[64],"reduce":[66],"complexity.":[69],"Note":[70],"that":[71],"proposed":[73],"approach":[74],"can":[75],"be":[76],"easily":[77],"generalized":[78],"rings":[81],"arbitrary":[83],"characteristic.":[84],"To":[85],"best":[87],"our":[89],"knowledge,":[90],"first":[94],"study":[95],"have":[97],"subquadratic":[99],"space":[100],"complexity":[101],"multiply":[103],"two":[104],"elements":[105],"rings.":[109]},"counts_by_year":[],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
