{"id":"https://openalex.org/W3124697227","doi":"https://doi.org/10.1109/tit.2021.3054612","title":"New Bounds and Constructions for Constant Weighted <i>X</i>-Codes","display_name":"New Bounds and Constructions for Constant Weighted <i>X</i>-Codes","publication_year":2021,"publication_date":"2021-01-26","ids":{"openalex":"https://openalex.org/W3124697227","doi":"https://doi.org/10.1109/tit.2021.3054612","mag":"3124697227"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3054612","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3054612","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/A5053562125","display_name":"Xiangliang Kong","orcid":"https://orcid.org/0000-0002-7893-2276"},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiangliang Kong","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, China","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100327797","display_name":"Xin Wang","orcid":"https://orcid.org/0000-0001-6364-8275"},"institutions":[{"id":"https://openalex.org/I3923682","display_name":"Soochow University","ror":"https://ror.org/05t8y2r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I3923682"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Wang","raw_affiliation_strings":["School of Mathematical Sciences, Soochow University, Suzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-6364-8275","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Soochow University, Suzhou, China","institution_ids":["https://openalex.org/I3923682"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029449317","display_name":"Gennian Ge","orcid":"https://orcid.org/0000-0002-1535-0754"},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gennian Ge","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1535-0754","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, China","institution_ids":["https://openalex.org/I96852419"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.2303,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51816052,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"67","issue":"4","first_page":"2181","last_page":"2191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11032","display_name":"VLSI and Analog Circuit Testing","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9987999796867371,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987000226974487,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.574713408946991},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44589921832084656},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4316929876804352},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.42104727029800415},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4080606698989868},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3628973364830017},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10840043425559998},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.06740069389343262}],"concepts":[{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.574713408946991},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44589921832084656},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4316929876804352},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42104727029800415},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4080606698989868},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3628973364830017},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10840043425559998},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.06740069389343262}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2021.3054612","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3054612","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/G3385502538","display_name":null,"funder_award_id":"11971325","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6052563824","display_name":null,"funder_award_id":"BK20180833","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G8396676344","display_name":null,"funder_award_id":"11801392","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/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W100035992","https://openalex.org/W1560011026","https://openalex.org/W1968160142","https://openalex.org/W2001779588","https://openalex.org/W2012584108","https://openalex.org/W2019294877","https://openalex.org/W2023158154","https://openalex.org/W2023600080","https://openalex.org/W2046549378","https://openalex.org/W2052723037","https://openalex.org/W2063273637","https://openalex.org/W2065341612","https://openalex.org/W2071474047","https://openalex.org/W2074920973","https://openalex.org/W2077263982","https://openalex.org/W2085160038","https://openalex.org/W2087289986","https://openalex.org/W2088622619","https://openalex.org/W2093276208","https://openalex.org/W2103813131","https://openalex.org/W2108348488","https://openalex.org/W2109594667","https://openalex.org/W2116747587","https://openalex.org/W2121325423","https://openalex.org/W2133322225","https://openalex.org/W2134959754","https://openalex.org/W2137806147","https://openalex.org/W2138693690","https://openalex.org/W2149459130","https://openalex.org/W2150075045","https://openalex.org/W2153336129","https://openalex.org/W2164604747","https://openalex.org/W2165030600","https://openalex.org/W2498848698","https://openalex.org/W2614184438","https://openalex.org/W2886156743","https://openalex.org/W2891402734","https://openalex.org/W2963846904","https://openalex.org/W3039692898","https://openalex.org/W3096775781","https://openalex.org/W3103914790","https://openalex.org/W6604055980","https://openalex.org/W6684527911","https://openalex.org/W6737889296","https://openalex.org/W7030635863"],"related_works":["https://openalex.org/W7606792","https://openalex.org/W8723561","https://openalex.org/W997982","https://openalex.org/W1871655","https://openalex.org/W6358082","https://openalex.org/W1017985","https://openalex.org/W2152706","https://openalex.org/W4934480","https://openalex.org/W4805079","https://openalex.org/W8558823"],"abstract_inverted_index":{"As":[0],"a":[1,13,36,100,178],"crucial":[2],"technique":[3],"for":[4,20,91,110,124,149,160,169,201],"integrated":[5],"circuits":[6],"(IC)":[7],"test":[8,25,80],"response":[9,26],"compaction,":[10],"X-compact":[11],"employs":[12],"special":[14,179],"kind":[15,203],"of":[16,23,30,47,52,82,107,114,181,199,204],"codes":[17],"called":[18],"X-codes":[19,48,51,94,152,182],"reliable":[21],"compressions":[22],"the":[24,28,79,83,104,125,132,161,170,190,196],"in":[27],"presence":[29],"unknown":[31],"logic":[32],"values":[33],"(Xs).":[34],"From":[35],"combinatorial":[37],"view":[38],"point,":[39],"Fujiwara":[40,185],"and":[41,49,59,89,117,129,141,155,166,186,188],"Colbourn":[42,187],"introduced":[43,183],"an":[44,65,111],"equivalent":[45],"definition":[46],"studied":[50],"small":[53],"weights":[54],"that":[55],"have":[56],"good":[57],"detectability":[58],"X-tolerance.":[60],"An":[61],"(m,n,d,x)":[62,112],"X-code":[63,113],"is":[64],"m\u00d7":[66],"n":[67,109],"binary":[68],"matrix":[69],"with":[70,127,153],"column":[71],"vectors":[72],"as":[73],"its":[74],"codewords.":[75],"The":[76],"parametersd,xcorrespond":[77],"to":[78],"quality":[81],"code.":[84],"In":[85],"this":[86,121,202],"paper,":[87],"bounds":[88],"constructions":[90,148],"constant":[92,150],"weighted":[93,151],"are":[95,158],"investigated.":[96],"First,":[97],"we":[98,118,144],"obtain":[99],"general":[101],"result":[102],"on":[103,195],"maximum":[105,197],"number":[106,198],"codewords":[108,200],"weight":[115],"w,":[116],"further":[119],"improve":[120,189],"lower":[122,193],"bound":[123,194],"case":[126,162,171],"x=2":[128],"w=3":[130],"through":[131],"probabilistic":[133],"method.":[134],"Then,":[135],"using":[136],"tools":[137],"from":[138],"additive":[139],"combinatorics":[140],"finite":[142],"fields,":[143],"present":[145],"some":[146],"explicit":[147],"d=3,7":[154],"x=2,":[156],"which":[157],"optimal":[159,168],"when":[163,172],"d=3,":[164,173],"w=4":[165],"nearly":[167],"w=3.":[174],"We":[175],"also":[176],"consider":[177],"class":[180],"by":[184],"best":[191],"known":[192],"X-codes.":[205]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
