{"id":"https://openalex.org/W2560746398","doi":"https://doi.org/10.1109/tit.2017.2742499","title":"Two New Families of Two-Weight Codes","display_name":"Two New Families of Two-Weight Codes","publication_year":2017,"publication_date":"2017-08-21","ids":{"openalex":"https://openalex.org/W2560746398","doi":"https://doi.org/10.1109/tit.2017.2742499","mag":"2560746398"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2017.2742499","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2742499","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1612.00967","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044196416","display_name":"Minjia Shi","orcid":"https://orcid.org/0000-0002-4990-6271"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]},{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Minjia Shi","raw_affiliation_strings":["National Mobile Communications Research Laboratory, Southeast University, Nanjing, China","School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"National Mobile Communications Research Laboratory, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100537186","display_name":"Yue Guan","orcid":"https://orcid.org/0000-0002-6356-3340"},"institutions":[{"id":"https://openalex.org/I143868143","display_name":"Anhui University","ror":"https://ror.org/05th6yx34","country_code":"CN","type":"education","lineage":["https://openalex.org/I143868143"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yue Guan","raw_affiliation_strings":["School of Mathematical Sciences, Anhui University, Hefei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Anhui University, Hefei, China","institution_ids":["https://openalex.org/I143868143"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024873890","display_name":"Patrick Sol\u00e9","orcid":"https://orcid.org/0000-0002-4078-8301"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210102686","display_name":"Laboratoire Analyse, G\u00e9om\u00e9trie et Applications","ror":"https://ror.org/018nzqy79","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210091279","https://openalex.org/I4210102686","https://openalex.org/I4210141950","https://openalex.org/I48825208"]},{"id":"https://openalex.org/I48825208","display_name":"Universit\u00e9 Paris 8","ror":"https://ror.org/04wez5e68","country_code":"FR","type":"education","lineage":["https://openalex.org/I48825208"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Patrick Sole","raw_affiliation_strings":["CNRS/LAGA, University of Paris 8, Saint-Denis, France"],"affiliations":[{"raw_affiliation_string":"CNRS/LAGA, University of Paris 8, Saint-Denis, France","institution_ids":["https://openalex.org/I48825208","https://openalex.org/I4210102686","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044196416"],"corresponding_institution_ids":["https://openalex.org/I143868143","https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":7.6849,"has_fulltext":false,"cited_by_count":85,"citation_normalized_percentile":{"value":0.9771887,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"63","issue":"10","first_page":"6240","last_page":"6246"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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":0.9997000098228455,"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/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6555671095848083},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.650702714920044},{"id":"https://openalex.org/keywords/weight-distribution","display_name":"Weight distribution","score":0.6293764710426331},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5876061916351318},{"id":"https://openalex.org/keywords/abelian-group","display_name":"Abelian group","score":0.5206350684165955},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4789855480194092},{"id":"https://openalex.org/keywords/secret-sharing","display_name":"Secret sharing","score":0.46615538001060486},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.46154502034187317},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4342499375343323},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.42876261472702026},{"id":"https://openalex.org/keywords/ring","display_name":"Ring (chemistry)","score":0.42537373304367065},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.3750251531600952},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.1789829432964325},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.1026620864868164},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08700096607208252},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08017703890800476}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6555671095848083},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.650702714920044},{"id":"https://openalex.org/C25432639","wikidata":"https://www.wikidata.org/wiki/Q3711790","display_name":"Weight distribution","level":2,"score":0.6293764710426331},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5876061916351318},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.5206350684165955},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4789855480194092},{"id":"https://openalex.org/C3087436","wikidata":"https://www.wikidata.org/wiki/Q1386603","display_name":"Secret sharing","level":3,"score":0.46615538001060486},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.46154502034187317},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4342499375343323},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.42876261472702026},{"id":"https://openalex.org/C2780378348","wikidata":"https://www.wikidata.org/wiki/Q25351438","display_name":"Ring (chemistry)","level":2,"score":0.42537373304367065},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.3750251531600952},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.1789829432964325},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1026620864868164},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08700096607208252},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08017703890800476},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2017.2742499","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2017.2742499","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:arXiv.org:1612.00967","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.00967","pdf_url":"https://arxiv.org/pdf/1612.00967","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"pmh:oai:HAL:hal-04089086v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04089086","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2017, 63 (10), pp.6240-6246. &#x27E8;10.1109/TIT.2017.2742499&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1612.00967","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1612.00967","pdf_url":"https://arxiv.org/pdf/1612.00967","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2683730091","display_name":null,"funder_award_id":"61672036","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2786739832","display_name":null,"funder_award_id":"2015D11","funder_id":"https://openalex.org/F4320324856","funder_display_name":"Southeast University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324856","display_name":"Southeast University","ror":"https://ror.org/04ct4d772"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1578199253","https://openalex.org/W1973483608","https://openalex.org/W2027062106","https://openalex.org/W2039466900","https://openalex.org/W2056890992","https://openalex.org/W2081016423","https://openalex.org/W2088023978","https://openalex.org/W2120756519","https://openalex.org/W2153988305","https://openalex.org/W2163834165","https://openalex.org/W2166231773","https://openalex.org/W2223285173","https://openalex.org/W2560684815","https://openalex.org/W2604096566","https://openalex.org/W2962947453","https://openalex.org/W6689310383"],"related_works":["https://openalex.org/W135568846","https://openalex.org/W2460434904","https://openalex.org/W1789159349","https://openalex.org/W2113911300","https://openalex.org/W2151857680","https://openalex.org/W4386066307","https://openalex.org/W832867880","https://openalex.org/W917159298","https://openalex.org/W1975697476","https://openalex.org/W2150591776"],"abstract_inverted_index":{"We":[0],"construct":[1],"two":[2,61],"new":[3],"infinite":[4,62],"families":[5,63],"of":[6,9,43,64,68,125,133],"trace":[7],"codes":[8,67,135],"dimension":[10],"2m,":[11],"over":[12],"the":[13,40,94,110,126,143],"ring":[14],"F":[15],"<sub":[16,21],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,22,28,73,77,82,86],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">p</sub>":[18,23],"+":[19],"uF":[20],",":[24],"with":[25],"u":[26],"<sup":[27,72,76,81,85],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[29,78,87],"=":[30,148],"u,":[31],"when":[32],"p":[33,105,147,155],"is":[34,50,91,102],"an":[35],"odd":[36,103],"prime.":[37],"They":[38],"have":[39],"algebraic":[41],"structure":[42],"abelian":[44],"codes.":[45,99],"Their":[46],"Lee":[47],"weight":[48],"distribution":[49],"computed":[51],"by":[52,123,142],"using":[53],"Gauss":[54],"sums.":[55],"By":[56],"Gray":[57],"mapping,":[58],"we":[59],"obtain":[60],"linear":[65],"p-ary":[66,114],"respective":[69],"lengths":[70],"(p":[71],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">m</sup>":[74,83],"-1)":[75,84],"and":[79,104,150,158],"2(p":[80],".":[88],"When":[89,100],"m":[90,101,151,159],"singly":[92],"even,":[93],"first":[95,111],"family":[96,112,131],"gives":[97],"five-weight":[98],"\u2261":[106],"3":[107,149],"(mod":[108],"4),":[109],"yields":[113],"two-weight":[115,134],"codes,":[116],"which":[117],"are":[118,137,167],"shown":[119,138],"to":[120,139,163],"be":[121,140],"optimal":[122],"application":[124],"Griesmer":[127,144],"bound.":[128],"The":[129],"second":[130],"consists":[132],"that":[136],"optimal,":[141],"bound,":[145],"whenever":[146],"\u2265":[152,156,160],"3,":[153],"or":[154],"5":[157],"4.":[161],"Applications":[162],"secret":[164],"sharing":[165],"schemes":[166],"given.":[168]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":15},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
