{"id":"https://openalex.org/W4386066307","doi":"https://doi.org/10.1109/isit54713.2023.10206921","title":"Characterization of All Optimal Finite-length Codes of Size Four for Binary Symmetric Channels","display_name":"Characterization of All Optimal Finite-length Codes of Size Four for Binary Symmetric Channels","publication_year":2023,"publication_date":"2023-06-25","ids":{"openalex":"https://openalex.org/W4386066307","doi":"https://doi.org/10.1109/isit54713.2023.10206921"},"language":"en","primary_location":{"id":"doi:10.1109/isit54713.2023.10206921","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5028927392","display_name":"Yanyan Dong","orcid":"https://orcid.org/0000-0002-6161-3455"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Yanyan Dong","raw_affiliation_strings":["National University of Singapore,Department of Electrical and Computer Engineering,Singapore","Department of Electrical and Computer Engineering, National University of Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore,Department of Electrical and Computer Engineering,Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Department of Electrical and Computer Engineering, National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054079306","display_name":"Shenghao Yang","orcid":"https://orcid.org/0000-0003-1987-5643"},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shenghao Yang","raw_affiliation_strings":["The Chinese University of Hong Kong, Shenzhen,School of Science and Engineering,Shenzhen,China","School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong, Shenzhen,School of Science and Engineering,Shenzhen,China","institution_ids":["https://openalex.org/I4210116924"]},{"raw_affiliation_string":"School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, Shenzhen, China","institution_ids":["https://openalex.org/I4210116924"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028927392"],"corresponding_institution_ids":["https://openalex.org/I165932596"],"apc_list":null,"apc_paid":null,"fwci":0.1592,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.59025369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"2135","last_page":"2140"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11321","display_name":"Error Correcting Code Techniques","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/T12162","display_name":"Cellular Automata and Applications","score":0.9991999864578247,"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/linear-code","display_name":"Linear code","score":0.8396905660629272},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.7553482055664062},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.6500273942947388},{"id":"https://openalex.org/keywords/reed\u2013muller-code","display_name":"Reed\u2013Muller code","score":0.6280118227005005},{"id":"https://openalex.org/keywords/expander-code","display_name":"Expander code","score":0.6213917136192322},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5653280019760132},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4586299955844879},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.4450336694717407},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.43721094727516174},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.42932072281837463},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4286918342113495},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.41426047682762146},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.397876501083374},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.38562747836112976},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.3482919931411743},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3096569776535034},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21705326437950134},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.10136991739273071}],"concepts":[{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.8396905660629272},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.7553482055664062},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.6500273942947388},{"id":"https://openalex.org/C169021753","wikidata":"https://www.wikidata.org/wiki/Q201972","display_name":"Reed\u2013Muller code","level":5,"score":0.6280118227005005},{"id":"https://openalex.org/C108509264","wikidata":"https://www.wikidata.org/wiki/Q5420758","display_name":"Expander code","level":5,"score":0.6213917136192322},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5653280019760132},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4586299955844879},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.4450336694717407},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.43721094727516174},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.42932072281837463},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4286918342113495},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.41426047682762146},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.397876501083374},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.38562747836112976},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.3482919931411743},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3096569776535034},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21705326437950134},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.10136991739273071},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit54713.2023.10206921","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit54713.2023.10206921","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1548479986","https://openalex.org/W2010444367","https://openalex.org/W2061169387","https://openalex.org/W2085603122","https://openalex.org/W2088208366","https://openalex.org/W2117476053","https://openalex.org/W2146368167","https://openalex.org/W2182112064","https://openalex.org/W2183449570","https://openalex.org/W2236569555","https://openalex.org/W3035292973","https://openalex.org/W3149455038","https://openalex.org/W6779885765"],"related_works":["https://openalex.org/W2041319252","https://openalex.org/W1976052006","https://openalex.org/W2476110915","https://openalex.org/W2098505542","https://openalex.org/W2121145816","https://openalex.org/W1992135520","https://openalex.org/W2124185731","https://openalex.org/W1966899942","https://openalex.org/W2095450438","https://openalex.org/W1992554485"],"abstract_inverted_index":{"The":[0],"search":[1],"for":[2,13,62,67,110,202,225],"optimal":[3,29,50,84,99,146,200],"finite-length":[4],"binary":[5,15,33],"block":[6],"codes":[7,30,34,41,51,58,61,88,100,106,109,123,126,138,142,147,168,217,221],"is":[8,83,94,154,199],"a":[9,79,111,119],"long-standing":[10],"open":[11],"problem":[12],"memoryless":[14],"symmetric":[16],"channels":[17],"(BSCs)":[18],"with":[19],"the":[20,28,47,53,87,102,130,145,152,181,203,215],"maximum":[21],"likelihood":[22],"decoding.":[23],"A":[24],"recent":[25],"work":[26],"studied":[27],"among":[31,85,218],"all":[32,86,144,214,219],"of":[35,49,56,89,104,121,133,148,222],"size":[36,90,149,223],"four,":[37],"including":[38],"both":[39],"linear":[40,57,80,105,209,220],"and":[42,45,59,107,127,136,139,187],"nonlinear":[43,122,167,197],"codes,":[44],"showed":[46],"existence":[48],"in":[52],"set":[54,103,131],"composed":[55,132],"Class-I":[60,108,135,173],"any":[63,226],"given":[64,227],"blocklength.":[65,113,228],"Furthermore,":[66],"blocklength":[68,153,160,182],"up":[69],"to":[70,157,171,185,208],"300,":[71],"it":[72,93],"has":[73],"been":[74],"shown":[75],"that":[76,82,129,164,177,195,205],"there":[77,97,165],"exists":[78],"code":[81,198],"four.":[91],"However,":[92],"unknown":[95],"whether":[96],"are":[98,166,178,206],"outside":[101],"general":[112],"In":[114],"this":[115],"paper,":[116],"we":[117,162,212],"derive":[118],"subset":[120],"called":[124],"Class-II":[125,137,175],"justify":[128],"linear,":[134,172],"their":[140],"equivalent":[141,170,207],"includes":[143],"four":[150,224],"when":[151],"not":[155,188],"equal":[156,189],"3.":[158],"For":[159,180],"3,":[161,190],"verify":[163],"(not":[169],"or":[174],"codes)":[176],"optimal.":[179],"from":[183],"2":[184],"300":[186],"our":[191],"computer":[192],"evaluations":[193],"show":[194],"no":[196],"except":[201],"ones":[204],"codes.":[210],"Moreover,":[211],"characterize":[213],"best":[216]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}