{"id":"https://openalex.org/W4312822986","doi":"https://doi.org/10.1109/tit.2022.3222474","title":"Infinite Families of Cyclic and Negacyclic Codes Supporting 3-Designs","display_name":"Infinite Families of Cyclic and Negacyclic Codes Supporting 3-Designs","publication_year":2022,"publication_date":"2022-11-16","ids":{"openalex":"https://openalex.org/W4312822986","doi":"https://doi.org/10.1109/tit.2022.3222474"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3222474","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3222474","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/A5073476855","display_name":"Xiaoqiang Wang","orcid":"https://orcid.org/0000-0001-7717-6133"},"institutions":[{"id":"https://openalex.org/I75900474","display_name":"Hubei University","ror":"https://ror.org/03a60m280","country_code":"CN","type":"education","lineage":["https://openalex.org/I75900474"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoqiang Wang","raw_affiliation_strings":["Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0001-7717-6133","affiliations":[{"raw_affiliation_string":"Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan, China","institution_ids":["https://openalex.org/I75900474"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054829854","display_name":"Chunming Tang","orcid":"https://orcid.org/0000-0001-9599-851X"},"institutions":[{"id":"https://openalex.org/I16351329","display_name":"China West Normal University","ror":"https://ror.org/04s99y476","country_code":"CN","type":"education","lineage":["https://openalex.org/I16351329"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunming Tang","raw_affiliation_strings":["School of Mathematics and Information, China West Normal University, Nanchong, China"],"raw_orcid":"https://orcid.org/0000-0001-9599-851X","affiliations":[{"raw_affiliation_string":"School of Mathematics and Information, China West Normal University, Nanchong, China","institution_ids":["https://openalex.org/I16351329"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074480584","display_name":"Cunsheng Ding","orcid":"https://orcid.org/0000-0001-9392-9860"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Cunsheng Ding","raw_affiliation_strings":["Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0001-9392-9860","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.3486,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.66089721,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"69","issue":"4","first_page":"2341","last_page":"2354"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9993000030517578,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9851999878883362,"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/notation","display_name":"Notation","score":0.7777884602546692},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.5446528792381287},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5279231071472168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5206990838050842},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5083748698234558},{"id":"https://openalex.org/keywords/number-theory","display_name":"Number theory","score":0.5079508423805237},{"id":"https://openalex.org/keywords/mathematical-notation","display_name":"Mathematical notation","score":0.47308093309402466},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42765721678733826},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3919967710971832},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3584306836128235},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.28596046566963196},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.21372359991073608},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.17154207825660706},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.16179275512695312},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06723642349243164}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7777884602546692},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.5446528792381287},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5279231071472168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5206990838050842},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5083748698234558},{"id":"https://openalex.org/C169654258","wikidata":"https://www.wikidata.org/wiki/Q12479","display_name":"Number theory","level":2,"score":0.5079508423805237},{"id":"https://openalex.org/C24457124","wikidata":"https://www.wikidata.org/wiki/Q1140046","display_name":"Mathematical notation","level":3,"score":0.47308093309402466},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42765721678733826},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3919967710971832},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3584306836128235},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.28596046566963196},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.21372359991073608},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17154207825660706},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.16179275512695312},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06723642349243164}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2022.3222474","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3222474","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:repository.hkust.edu.hk:1783.1-124944","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-124944","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"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":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2991662888","display_name":"Constacyclic codes over finite fields","funder_award_id":"16301522","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G5072621123","display_name":null,"funder_award_id":"11871058","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8792667394","display_name":null,"funder_award_id":"12001175","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W15446469","https://openalex.org/W584522352","https://openalex.org/W2015337464","https://openalex.org/W2031487769","https://openalex.org/W2039466900","https://openalex.org/W2039739591","https://openalex.org/W2095243060","https://openalex.org/W2110353549","https://openalex.org/W2118897868","https://openalex.org/W2120756519","https://openalex.org/W2984241739","https://openalex.org/W2996205462","https://openalex.org/W2996271523","https://openalex.org/W3022561029","https://openalex.org/W3094527023","https://openalex.org/W3131307612","https://openalex.org/W3175644973","https://openalex.org/W3199390557","https://openalex.org/W3205470690","https://openalex.org/W4205233257","https://openalex.org/W4205545339","https://openalex.org/W4206775542","https://openalex.org/W4214828742","https://openalex.org/W6800077898"],"related_works":["https://openalex.org/W2393607213","https://openalex.org/W2495832077","https://openalex.org/W1968256718","https://openalex.org/W2624682093","https://openalex.org/W98357545","https://openalex.org/W2278797713","https://openalex.org/W4249487612","https://openalex.org/W977407476","https://openalex.org/W3167735904","https://openalex.org/W4280602899"],"abstract_inverted_index":{"Interplay":[0],"between":[1],"coding":[2,17],"theory":[3],"and":[4,16,96,112,148],"combinatorial$t$-designs":[5],"has":[6,51],"been":[7,31,52],"a":[8,146],"hot":[9],"topic":[10],"for":[11,14],"many":[12],"years":[13],"combinatorialists":[15],"theorists.":[18],"Some":[19],"infinite":[20,26,40,47,84,92,98,106,132],"families":[21,27,99,107,133],"of":[22,28,42,49,62,77,86,94,100,108,116,124,134],"cyclic":[23,87],"codes":[24,44,88,102,118,127,137],"supporting":[25,45],"3-designs":[29,50,95],"have":[30],"constructed":[32],"in":[33,54,155],"the":[34,55,59,113],"past":[35],"50":[36],"years.":[37],"However,":[38],"no":[39],"family":[41,48,85,93],"negacyclic":[43,101,126],"an":[46,67,73,83,91],"reported":[53],"literature.":[56],"This":[57],"is":[58,80],"main":[60],"motivation":[61],"this":[63,78,156],"paper.":[64,157],"Let$q=p^{m}$,":[65],"where$p$is":[66],"odd":[68],"prime":[69],"and$m":[70],"\\geq":[71],"2$is":[72],"integer.":[74],"The":[75,110,121],"objective":[76],"paper":[79],"to":[81],"present":[82],"over${\\mathrm":[89,103,128,144],"{GF}}(q)$supporting":[90],"two":[97,105],"{GF}}(q^{2})$supporting":[104],"3-designs.":[109],"parameters":[111],"weight":[114],"distributions":[115],"these":[117,125],"are":[119,138,152],"determined.":[120],"subfield":[122],"subcodes":[123],"{GF}}(q)$are":[129],"studied.":[130],"Three":[131],"almost":[135],"MDS":[136],"also":[139,153],"presented.":[140],"A":[141],"constacyclic":[142],"code":[143],"{GF}}(4)$supporting":[145],"4-design":[147],"seven":[149],"open":[150],"problems":[151],"presented":[154]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-08-04T08:18:43.703281","created_date":"2025-10-10T00:00:00"}
