{"id":"https://openalex.org/W3175644973","doi":"https://doi.org/10.1109/tit.2022.3156072","title":"Infinite Families of Linear Codes Supporting More <i>t</i>-Designs","display_name":"Infinite Families of Linear Codes Supporting More <i>t</i>-Designs","publication_year":2022,"publication_date":"2022-03-02","ids":{"openalex":"https://openalex.org/W3175644973","doi":"https://doi.org/10.1109/tit.2022.3156072","mag":"3175644973"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3156072","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3156072","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/A5006398204","display_name":"Qianqian Yan","orcid":null},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qianqian Yan","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-8215-0242","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019035079","display_name":"Junling Zhou","orcid":"https://orcid.org/0000-0002-5725-4920"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junling Zhou","raw_affiliation_strings":["Department of Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-5725-4920","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006398204"],"corresponding_institution_ids":["https://openalex.org/I21193070"],"apc_list":null,"apc_paid":null,"fwci":1.526,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.84822557,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"68","issue":"7","first_page":"4365","last_page":"4377"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9930999875068665,"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":0.9887999892234802,"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/notation","display_name":"Notation","score":0.6924149394035339},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5046242475509644},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.46360740065574646},{"id":"https://openalex.org/keywords/bch-code","display_name":"BCH code","score":0.41764557361602783},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.36551129817962646},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3553101420402527},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29939258098602295},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.23580798506736755},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.162176251411438},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.13399401307106018}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6924149394035339},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5046242475509644},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.46360740065574646},{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.41764557361602783},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.36551129817962646},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3553101420402527},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29939258098602295},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.23580798506736755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.162176251411438},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.13399401307106018}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3156072","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3156072","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1340580136","display_name":null,"funder_award_id":"11971053","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2401255269","display_name":null,"funder_award_id":"1222013","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G4918365906","display_name":null,"funder_award_id":"12171028","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/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W1519782116","https://openalex.org/W1530125006","https://openalex.org/W1559343931","https://openalex.org/W1981676191","https://openalex.org/W1991423464","https://openalex.org/W1993191758","https://openalex.org/W2020484625","https://openalex.org/W2044703300","https://openalex.org/W2327031263","https://openalex.org/W2808611543","https://openalex.org/W2991466664","https://openalex.org/W2996205462","https://openalex.org/W3022561029","https://openalex.org/W3094527023","https://openalex.org/W3119473442","https://openalex.org/W3164275531","https://openalex.org/W4206775542"],"related_works":["https://openalex.org/W1978042415","https://openalex.org/W3086542228","https://openalex.org/W2017331178","https://openalex.org/W2976797620","https://openalex.org/W347180939","https://openalex.org/W3046926816","https://openalex.org/W3083539681","https://openalex.org/W2530212042","https://openalex.org/W2332694326","https://openalex.org/W4249089511"],"abstract_inverted_index":{"Tang":[0],"and":[1,21,32,68,118,211],"Ding":[2],"[IEEE":[3],"IT":[4],"67":[5],"(2021)":[6],"244-254]":[7],"studied":[8],"the":[9,35,38,41,58,61,182,187,220,223,236],"class":[10,151],"of":[11,37,60,73,95,137,152],"BCH":[12],"codes":[13,24,47,67,200],"<inline-formula":[14,26,74,82,99,110,124,139,153,171,191,204,229],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[15,27,75,83,100,111,125,140,154,172,192,205,230],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[16,28,76,84,101,112,126,141,155,173,193,206,231],"<tex-math":[17,29,77,85,102,113,127,142,156,174,194,207,232],"notation=\"LaTeX\">$\\mathcal":[18,103],"{C}_{(q,q+1,4,1)}$":[19,104],"</tex-math></inline-formula>":[20,31,79,87,105,117,131,144,158,177,196,209,234],"their":[22],"dual":[23],"with":[25,81,146,168],"notation=\"LaTeX\">$q=2^{m}$":[30],"established":[33],"that":[34,93],"codewords":[36,59,94],"minimum":[39],"(or":[40],"second":[42],"minimum)":[43],"weight":[44,64,96],"in":[45,65,98,162,242],"these":[46,179],"support":[48,106,120],"4-designs":[49,107,221],"or":[50],"3-designs.":[51],"Motivated":[52],"by":[53,240],"this,":[54],"we":[55,91,160],"further":[56,214],"investigate":[57],"next":[62],"adjacent":[63],"such":[66],"discover":[69],"more":[70],"infinite":[71,135],"classes":[72,136],"notation=\"LaTeX\">$t$":[78,143,157],"-designs":[80,145,159],"notation=\"LaTeX\">$t=3,4$":[86],".":[88],"In":[89],"particular,":[90],"prove":[92],"7":[97],"for":[108,122,201],"odd":[109],"notation=\"LaTeX\">$m":[114,128],"\\geqslant":[115,129],"5$":[116],"they":[119,212],"3-designs":[121],"even":[123],"4$":[130],",":[132],"which":[133],"provide":[134],"simple":[138,189],"new":[147],"parameters.":[148],"Another":[149],"significant":[150],"produce":[161],"this":[163],"paper":[164],"has":[165],"complementary":[166],"designs":[167,180,197],"parameters":[169],"4-":[170,190],"notation=\"LaTeX\">$(2^{2s+1}+":[175],"1,5,5)$":[176],";":[178,210],"have":[181],"smallest":[183],"index":[184],"among":[185],"all":[186],"known":[188],"notation=\"LaTeX\">$(q+1,5,\\lambda)$":[195],"derived":[198],"from":[199],"prime":[202],"powers":[203],"notation=\"LaTeX\">$q$":[208],"are":[213],"proved":[215],"to":[216,219],"be":[217],"isomorphic":[218],"admitting":[222],"projective":[224],"general":[225],"linear":[226],"group":[227,238],"PGL":[228],"notation=\"LaTeX\">$(2,2^{2s+1})$":[233],"as":[235],"automorphism":[237],"constructed":[239],"Alltop":[241],"1969.":[243]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
