{"id":"https://openalex.org/W4403511655","doi":"https://doi.org/10.1109/tit.2024.3482726","title":"On the b-Symbol Distances of Matrix Product Codes, Constacyclic Codes, and Reed-Muller Codes","display_name":"On the b-Symbol Distances of Matrix Product Codes, Constacyclic Codes, and Reed-Muller Codes","publication_year":2024,"publication_date":"2024-10-17","ids":{"openalex":"https://openalex.org/W4403511655","doi":"https://doi.org/10.1109/tit.2024.3482726"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3482726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3482726","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","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/A5011652154","display_name":"Xu Pan","orcid":"https://orcid.org/0000-0003-2391-3892"},"institutions":[{"id":"https://openalex.org/I159948400","display_name":"Jinan University","ror":"https://ror.org/02xe5ns62","country_code":"CN","type":"education","lineage":["https://openalex.org/I159948400"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xu Pan","raw_affiliation_strings":["School of Information Science and Technology/Cyber Security, Jinan University, Guangzhou, Guangdong, China"],"raw_orcid":"https://orcid.org/0000-0003-2391-3892","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology/Cyber Security, Jinan University, Guangzhou, Guangdong, China","institution_ids":["https://openalex.org/I159948400"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063268716","display_name":"San Ling","orcid":"https://orcid.org/0000-0002-1978-3557"},"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":"San Ling","raw_affiliation_strings":["School of Physical and Mathematical Sciences, Nanyang Technological University, Jurong West, Singapore","School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-1978-3557","affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]},{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079255508","display_name":"Hongwei Liu","orcid":"https://orcid.org/0000-0003-3503-8220"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Key Laboratory NAA-MOE, Central China Normal University, Wuhan, China","School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China"],"raw_orcid":"https://orcid.org/0000-0003-3503-8220","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Key Laboratory NAA-MOE, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Central China Normal University, Wuhan, Hubei, China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081545653","display_name":"Bocong Chen","orcid":"https://orcid.org/0000-0001-5295-8403"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bocong Chen","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou, Guangdong, China"],"raw_orcid":"https://orcid.org/0000-0001-5295-8403","affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou, Guangdong, China","institution_ids":["https://openalex.org/I90610280"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5557,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.72470392,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"71","issue":"1","first_page":"287","last_page":"296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9984999895095825,"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":0.9984999895095825,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9832000136375427,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9778000116348267,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.6656625270843506},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.6243458986282349},{"id":"https://openalex.org/keywords/symbol","display_name":"Symbol (formal)","score":0.5790896415710449},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5314090847969055},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.5206693410873413},{"id":"https://openalex.org/keywords/reed\u2013solomon-error-correction","display_name":"Reed\u2013Solomon error correction","score":0.4997396469116211},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.4411693215370178},{"id":"https://openalex.org/keywords/fountain-code","display_name":"Fountain code","score":0.44032636284828186},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43630021810531616},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43603378534317017},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.434173583984375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4269993007183075},{"id":"https://openalex.org/keywords/hamming-code","display_name":"Hamming code","score":0.4237546920776367},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.42169299721717834},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.41503798961639404},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.40428534150123596},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.387604296207428},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.35423803329467773},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32636556029319763}],"concepts":[{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.6656625270843506},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.6243458986282349},{"id":"https://openalex.org/C134400042","wikidata":"https://www.wikidata.org/wiki/Q2372244","display_name":"Symbol (formal)","level":2,"score":0.5790896415710449},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5314090847969055},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.5206693410873413},{"id":"https://openalex.org/C78065487","wikidata":"https://www.wikidata.org/wiki/Q1061598","display_name":"Reed\u2013Solomon error correction","level":5,"score":0.4997396469116211},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.4411693215370178},{"id":"https://openalex.org/C76132124","wikidata":"https://www.wikidata.org/wiki/Q5474786","display_name":"Fountain code","level":5,"score":0.44032636284828186},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43630021810531616},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43603378534317017},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.434173583984375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4269993007183075},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.4237546920776367},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.42169299721717834},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.41503798961639404},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.40428534150123596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.387604296207428},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.35423803329467773},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32636556029319763},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2024.3482726","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3482726","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:dr.ntu.edu.sg:10356/217929","is_oa":false,"landing_page_url":"https://hdl.handle.net/10356/217929","pdf_url":null,"source":{"id":"https://openalex.org/S4306402609","display_name":"DR-NTU (Nanyang Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172675005","host_organization_name":"Nanyang Technological University","host_organization_lineage":["https://openalex.org/I172675005"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2839263876","display_name":null,"funder_award_id":"12401689","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3915287093","display_name":null,"funder_award_id":"30106220482","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5029367723","display_name":null,"funder_award_id":"12171191","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5300754835","display_name":null,"funder_award_id":"04INS000047C230GRT01","funder_id":"https://openalex.org/F4320320766","funder_display_name":"Nanyang Technological University"},{"id":"https://openalex.org/G8035838337","display_name":null,"funder_award_id":"12271199","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1606480398","https://openalex.org/W1917095352","https://openalex.org/W1995763034","https://openalex.org/W2021828617","https://openalex.org/W2027190808","https://openalex.org/W2045558951","https://openalex.org/W2049767466","https://openalex.org/W2058283536","https://openalex.org/W2073236804","https://openalex.org/W2092031626","https://openalex.org/W2105996438","https://openalex.org/W2112742311","https://openalex.org/W2130479486","https://openalex.org/W2297946362","https://openalex.org/W2506139267","https://openalex.org/W2526251771","https://openalex.org/W2735920813","https://openalex.org/W2783897521","https://openalex.org/W2955690944","https://openalex.org/W2963311024","https://openalex.org/W2964265029","https://openalex.org/W2974932074","https://openalex.org/W2998120784","https://openalex.org/W3011811589","https://openalex.org/W3141363917","https://openalex.org/W3203115850","https://openalex.org/W3206876133","https://openalex.org/W3208635886","https://openalex.org/W4286817187","https://openalex.org/W4312233383","https://openalex.org/W4312777099","https://openalex.org/W4312902179","https://openalex.org/W4322733327","https://openalex.org/W4400320279","https://openalex.org/W4400352020","https://openalex.org/W7021089026"],"related_works":["https://openalex.org/W2976106059","https://openalex.org/W2060232182","https://openalex.org/W2296600582","https://openalex.org/W4245031194","https://openalex.org/W2089476296","https://openalex.org/W1985033232","https://openalex.org/W2017830967","https://openalex.org/W2289440727","https://openalex.org/W2348551008","https://openalex.org/W2124185731"],"abstract_inverted_index":{"Matrix":[0],"product":[1,30,66,115],"codes":[2,14,102,139],"are":[3,84],"generalizations":[4],"of":[5,9,27,43,46,64,72,94,125,137,144],"some":[6,71],"well-known":[7],"classes":[8],"codes,":[10,67,116],"including":[11],"generalized":[12],"Reed-Muller":[13,138],"and":[15,56,117],"repeated-root":[16],"constacyclic":[17,101,127],"codes.":[18,49,128],"Recently,":[19],"a":[20,28,141],"bound":[21],"for":[22,59],"the":[23,41,60,73,82,121,133,145],"minimum":[24,61,122,134],"symbol-pair":[25,48],"distance":[26,63,124],"matrix":[29,65,114],"code":[31],"was":[32],"given":[33],"by":[34,75],"(Luo":[35,76],"et":[36,77],"al.,":[37,78],"2023),":[38],"leading":[39],"to":[40,86],"creation":[42],"new":[44,96,146],"families":[45],"MDS":[47],"In":[50],"this":[51],"paper,":[52],"we":[53,98,130],"provide":[54],"lower":[55],"upper":[57],"bounds":[58,83,119],"b-symbol":[62,123,135],"which":[68],"naturally":[69],"extends":[70],"results":[74],"2023).":[79],"Examples":[80],"meeting":[81,106],"included":[85],"illustrate":[87],"our":[88],"results.":[89],"As":[90],"an":[91],"initial":[92],"application":[93,143],"these":[95],"bounds,":[97],"establish":[99],"that":[100],"(repeated-root":[103],"or":[104],"otherwise)":[105],"specific":[107],"criteria":[108],"can":[109],"indeed":[110],"be":[111],"classified":[112],"as":[113,140],"present":[118],"on":[120],"such":[126],"Additionally,":[129],"determine":[131],"all":[132],"distances":[136],"secondary":[142],"bounds.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2025-12-27T23:08:20.325037","created_date":"2024-10-18T00:00:00"}
