{"id":"https://openalex.org/W3191181309","doi":"https://doi.org/10.1587/transfun.2021tap0010","title":"Linking Reversed and Dual Codes of Quasi-Cyclic Codes","display_name":"Linking Reversed and Dual Codes of Quasi-Cyclic Codes","publication_year":2021,"publication_date":"2021-07-29","ids":{"openalex":"https://openalex.org/W3191181309","doi":"https://doi.org/10.1587/transfun.2021tap0010","mag":"3191181309"},"language":"en","primary_location":{"id":"doi:10.1587/transfun.2021tap0010","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transfun.2021tap0010","pdf_url":"https://www.jstage.jst.go.jp/article/transfun/E105.A/3/E105.A_2021TAP0010/_pdf","source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.jstage.jst.go.jp/article/transfun/E105.A/3/E105.A_2021TAP0010/_pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031290175","display_name":"Ramy Taki Eldin","orcid":"https://orcid.org/0000-0003-4184-9222"},"institutions":[{"id":"https://openalex.org/I107720978","display_name":"Ain Shams University","ror":"https://ror.org/00cb9w016","country_code":"EG","type":"education","lineage":["https://openalex.org/I107720978"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"Ramy TAKI ELDIN","raw_affiliation_strings":["Faculty of Engineering, Ain Shams University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering, Ain Shams University","institution_ids":["https://openalex.org/I107720978"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006877645","display_name":"Hajime Matsui","orcid":"https://orcid.org/0000-0003-4778-8045"},"institutions":[{"id":"https://openalex.org/I4840577","display_name":"Toyota Technological Institute","ror":"https://ror.org/001hv0k59","country_code":"JP","type":"education","lineage":["https://openalex.org/I4840577"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Hajime MATSUI","raw_affiliation_strings":["Toyota Technological Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Toyota Technological Institute","institution_ids":["https://openalex.org/I4840577"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.134,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57512928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"E105.A","issue":"3","first_page":"381","last_page":"388"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9994999766349792,"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/T12029","display_name":"DNA and Biological Computing","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9958000183105469,"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/generator-matrix","display_name":"Generator matrix","score":0.7663497924804688},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6317276358604431},{"id":"https://openalex.org/keywords/polynomial-code","display_name":"Polynomial code","score":0.6144689917564392},{"id":"https://openalex.org/keywords/dual-code","display_name":"Dual code","score":0.613868772983551},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.6106584668159485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5612986087799072},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5548216700553894},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5292341709136963},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5063415765762329},{"id":"https://openalex.org/keywords/cyclic-code","display_name":"Cyclic code","score":0.5033475756645203},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.49353015422821045},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.47345417737960815},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4690447449684143},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45864158868789673},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2885957360267639},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23692944645881653},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15935662388801575},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14943012595176697},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.14795821905136108},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1274021863937378},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.09590417146682739}],"concepts":[{"id":"https://openalex.org/C1842014","wikidata":"https://www.wikidata.org/wiki/Q1502046","display_name":"Generator matrix","level":3,"score":0.7663497924804688},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6317276358604431},{"id":"https://openalex.org/C39635130","wikidata":"https://www.wikidata.org/wiki/Q7226636","display_name":"Polynomial code","level":5,"score":0.6144689917564392},{"id":"https://openalex.org/C73666251","wikidata":"https://www.wikidata.org/wiki/Q5310189","display_name":"Dual code","level":5,"score":0.613868772983551},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6106584668159485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5612986087799072},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5548216700553894},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5292341709136963},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5063415765762329},{"id":"https://openalex.org/C2096984","wikidata":"https://www.wikidata.org/wiki/Q245464","display_name":"Cyclic code","level":5,"score":0.5033475756645203},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.49353015422821045},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.47345417737960815},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4690447449684143},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45864158868789673},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2885957360267639},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23692944645881653},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15935662388801575},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14943012595176697},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.14795821905136108},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1274021863937378},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.09590417146682739},{"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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":1,"locations":[{"id":"doi:10.1587/transfun.2021tap0010","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transfun.2021tap0010","pdf_url":"https://www.jstage.jst.go.jp/article/transfun/E105.A/3/E105.A_2021TAP0010/_pdf","source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1587/transfun.2021tap0010","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transfun.2021tap0010","pdf_url":"https://www.jstage.jst.go.jp/article/transfun/E105.A/3/E105.A_2021TAP0010/_pdf","source":{"id":"https://openalex.org/S166990724","display_name":"IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences","issn_l":"0916-8508","issn":["0916-8508","1745-1337"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2744654132","display_name":"On relations between error correcting codes and multi-valued logic functions via discrete Fourier transforms","funder_award_id":"19K22850","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3191181309.pdf","grobid_xml":"https://content.openalex.org/works/W3191181309.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W2004846426","https://openalex.org/W2055688407","https://openalex.org/W2082540760","https://openalex.org/W2129910432","https://openalex.org/W2155842274","https://openalex.org/W2217792622","https://openalex.org/W2587975760","https://openalex.org/W2947397991","https://openalex.org/W2994989107","https://openalex.org/W2998288983","https://openalex.org/W3047141276","https://openalex.org/W3087805872","https://openalex.org/W3138936470","https://openalex.org/W4212825216"],"related_works":["https://openalex.org/W2771127828","https://openalex.org/W1579051351","https://openalex.org/W1989332790","https://openalex.org/W4312970405","https://openalex.org/W2111330432","https://openalex.org/W197575802","https://openalex.org/W4248511311","https://openalex.org/W1996066298","https://openalex.org/W2099549796","https://openalex.org/W1978124453"],"abstract_inverted_index":{"It":[0],"is":[1,20,43,59,111,166],"known":[2],"that":[3,170,179],"quasi-cyclic":[4],"(QC)":[5],"codes":[6,160,178],"over":[7],"the":[8,44,54,120,156,181,185],"finite":[9],"field":[10],"\ud835\udd3dq":[11],"correspond":[12],"to":[13,108,134,155,168],"certain":[14],"\ud835\udd3dq[x]-modules.":[15],"A":[16,101],"QC":[17,159,177],"code":[18,37,45,56],"C":[19,31,52,58,65,107,142],"specified":[21],"by":[22,41,47,61],"a":[23,86,95],"generator":[24,96],"polynomial":[25,97],"matrix":[26,98],"G":[27,132],"whose":[28],"rows":[29],"generate":[30],"as":[32],"an":[33,91,148],"\ud835\udd3dq[x]-module.":[34],"The":[35],"reversed":[36],"of":[38,51,57,99,158,188],"C,":[39,73,76,80,88,123],"denoted":[40,60],"R,":[42,124,137,140],"obtained":[46],"reversing":[48],"all":[49],"codewords":[50],"while":[53],"dual":[55],"C\u22a5.":[62,126,146],"We":[63],"call":[64],"reversible,":[66],"self-orthogonal,":[67],"and":[68,77,103,125,141],"self-dual":[69],"if":[70],"R":[71,144],"=":[72,79,143,145],"C\u22a5":[74,78,135,138],"\u2287":[75,136],"respectively.":[81],"In":[82,116],"this":[83,114],"study,":[84],"for":[85,94,106],"given":[87],"we":[89,118,128,150],"find":[90],"explicit":[92],"formula":[93],"R.":[100],"necessary":[102],"sufficient":[104],"condition":[105],"be":[109],"reversible":[110,175],"derived":[112],"from":[113],"formula.":[115],"addition,":[117],"reveal":[119],"relations":[121],"among":[122],"Specifically,":[127],"give":[129],"conditions":[130],"on":[131,184],"corresponding":[133],"\u2286":[139],"As":[147],"application,":[149],"employ":[151],"these":[152],"theoretical":[153],"results":[154],"construction":[157],"with":[161],"best":[162],"parameters.":[163],"Computer":[164],"search":[165],"used":[167],"show":[169],"there":[171],"exist":[172],"various":[173],"binary":[174],"self-orthogonal":[176],"achieve":[180],"upper":[182],"bounds":[183],"minimum":[186],"distance":[187],"linear":[189],"codes.":[190]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
