{"id":"https://openalex.org/W2996205462","doi":"https://doi.org/10.1109/tit.2019.2959764","title":"Codes, Differentially $\\delta$ -Uniform Functions, and $t$ -Designs","display_name":"Codes, Differentially $\\delta$ -Uniform Functions, and $t$ -Designs","publication_year":2019,"publication_date":"2019-12-17","ids":{"openalex":"https://openalex.org/W2996205462","doi":"https://doi.org/10.1109/tit.2019.2959764","mag":"2996205462"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2019.2959764","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2959764","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/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"]},{"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":["CN","HK"],"is_corresponding":false,"raw_author_name":"Chunming Tang","raw_affiliation_strings":["Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong","School of Mathematics and Information, China West Normal University, Nanchong, China"],"raw_orcid":"https://orcid.org/0000-0001-9599-851X","affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, The Hong Kong University of Science and Technology, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"School of Mathematics and Information, China West Normal University, Nanchong, China","institution_ids":["https://openalex.org/I16351329"]}]},{"author_position":"middle","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"],"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","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066461623","display_name":"Maosheng Xiong","orcid":"https://orcid.org/0000-0001-6044-9561"},"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":"Maosheng Xiong","raw_affiliation_strings":["Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong"],"raw_orcid":"https://orcid.org/0000-0001-6044-9561","affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong","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":3.6155,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.94509483,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"66","issue":"6","first_page":"3691","last_page":"3703"},"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":0.9995999932289124,"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/T10849","display_name":"Finite Group Theory Research","score":0.9923999905586243,"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/mathematics","display_name":"Mathematics","score":0.6605017781257629},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.6532472372055054},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.6024773120880127},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.5846718549728394},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.5377410054206848},{"id":"https://openalex.org/keywords/steiner-system","display_name":"Steiner system","score":0.5215734839439392},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5089700222015381},{"id":"https://openalex.org/keywords/combinatorial-design","display_name":"Combinatorial design","score":0.5007205009460449},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.48250246047973633},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4308667778968811},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4294973611831665},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38245245814323425},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.2974209189414978},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2303638458251953},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.23004579544067383},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.20098936557769775},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.1434083878993988}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6605017781257629},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.6532472372055054},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.6024773120880127},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.5846718549728394},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.5377410054206848},{"id":"https://openalex.org/C175695255","wikidata":"https://www.wikidata.org/wiki/Q4420916","display_name":"Steiner system","level":2,"score":0.5215734839439392},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5089700222015381},{"id":"https://openalex.org/C122451846","wikidata":"https://www.wikidata.org/wiki/Q5150824","display_name":"Combinatorial design","level":2,"score":0.5007205009460449},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.48250246047973633},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4308667778968811},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4294973611831665},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38245245814323425},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.2974209189414978},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2303638458251953},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.23004579544067383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.20098936557769775},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.1434083878993988},{"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/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.2019.2959764","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2019.2959764","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.ust.hk:1783.1-104015","is_oa":false,"landing_page_url":"http://www.scopus.com/record/display.url?eid=2-s2.0-85086237578&origin=inward","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":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3413057548","display_name":null,"funder_award_id":"NHKUST619/17","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G393080029","display_name":null,"funder_award_id":"CXTD2014-4","funder_id":"https://openalex.org/F4320324420","funder_display_name":"China West Normal University"},{"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/G6668725646","display_name":null,"funder_award_id":"14E013","funder_id":"https://openalex.org/F4320324420","funder_display_name":"China West Normal University"},{"id":"https://openalex.org/G8829760363","display_name":null,"funder_award_id":"16300418","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"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"},{"id":"https://openalex.org/F4320324420","display_name":"China West Normal University","ror":"https://ror.org/04s99y476"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W27322304","https://openalex.org/W584522352","https://openalex.org/W1550528471","https://openalex.org/W1556782625","https://openalex.org/W1559343931","https://openalex.org/W1587687098","https://openalex.org/W1606480398","https://openalex.org/W1979946760","https://openalex.org/W2008192074","https://openalex.org/W2015337464","https://openalex.org/W2018029151","https://openalex.org/W2022609823","https://openalex.org/W2033288454","https://openalex.org/W2044983034","https://openalex.org/W2063177615","https://openalex.org/W2067964515","https://openalex.org/W2094600995","https://openalex.org/W2120756519","https://openalex.org/W2162542560","https://openalex.org/W2488283090","https://openalex.org/W2808611543","https://openalex.org/W2809498776","https://openalex.org/W2905157631","https://openalex.org/W2920427034","https://openalex.org/W2942941259","https://openalex.org/W2950788636","https://openalex.org/W2963030145","https://openalex.org/W2964020194","https://openalex.org/W2964272634","https://openalex.org/W2987248294","https://openalex.org/W3193541866","https://openalex.org/W4206775542","https://openalex.org/W4211147273","https://openalex.org/W4236140721","https://openalex.org/W4244155401","https://openalex.org/W6633362994","https://openalex.org/W6800077898"],"related_works":["https://openalex.org/W2048590019","https://openalex.org/W1522223029","https://openalex.org/W1980807369","https://openalex.org/W2064878508","https://openalex.org/W11591861","https://openalex.org/W2962836269","https://openalex.org/W4211147273","https://openalex.org/W3083124347","https://openalex.org/W2964502204","https://openalex.org/W2996205462"],"abstract_inverted_index":{"Boolean":[0],"functions,":[1],"coding":[2],"theory":[3,90,109],"and":[4,9,30,65,95,100,112,128,133,137,150,158],"t-designs":[5,17,119],"have":[6],"close":[7],"connections":[8],"interesting":[10],"interplay.":[11],"A":[12],"standard":[13],"approach":[14],"to":[15,87],"constructing":[16],"is":[18,86,120,126,139],"the":[19,31,59,62],"use":[20],"of":[21,77,83,115],"linear":[22,50,116],"codes":[23,51,94,99,114,117,146],"with":[24,147],"certain":[25],"regularity.":[26],"The":[27,80],"Assmus-Mattson":[28,63,124],"Theorem":[29,64],"automorphism":[32],"groups":[33],"are":[34,154,168],"two":[35],"ways":[36],"for":[37,45,91,110],"proving":[38],"that":[39],"a":[40,69,75,89,107,122,129],"code":[41],"has":[42],"sufficient":[43],"regularity":[44],"supporting":[46,118],"t-designs.":[47,103],"However,":[48],"some":[49],"hold":[52],"t-designs,":[53],"although":[54],"they":[55],"do":[56,66],"not":[57,67],"satisfy":[58],"conditions":[60],"in":[61,170],"admit":[68],"t-transitive":[70],"or":[71],"t-homogeneous":[72],"group":[73],"as":[74],"subgroup":[76],"their":[78],"automorphisms.":[79],"major":[81],"objective":[82],"this":[84,105,171],"paper":[85],"develop":[88],"explaining":[92],"such":[93,97],"obtaining":[96],"new":[98,102,148,156],"hence":[101],"To":[104],"end,":[106],"general":[108,143],"punctured":[111],"shortened":[113],"established,":[121],"generalized":[123],"theorem":[125],"developed,":[127],"link":[130],"between":[131],"2-designs":[132,138,157],"differentially":[134],"\u03b4-uniform":[135],"functions":[136],"built.":[140],"With":[141],"these":[142],"results,":[144],"binary":[145],"parameters":[149],"explicit":[151],"weight":[152],"distributions":[153],"obtained,":[155],"Steiner":[159],"system":[160],"S(2,":[161],"4,":[162],"2":[163],"<sup":[164],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[165],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</sup>":[166],")":[167],"produced":[169],"paper.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":4}],"updated_date":"2026-06-18T10:00:31.954636","created_date":"2019-12-26T00:00:00"}