{"id":"https://openalex.org/W2147955754","doi":"https://doi.org/10.1109/tit.1973.1055086","title":"On majority-logic-decodable arithmetic codes","display_name":"On majority-logic-decodable arithmetic codes","publication_year":1973,"publication_date":"1973-09-01","ids":{"openalex":"https://openalex.org/W2147955754","doi":"https://doi.org/10.1109/tit.1973.1055086","mag":"2147955754"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1973.1055086","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1973.1055086","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/A5028104710","display_name":"Chin-Long Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chin-Long Chen","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021730223","display_name":"R. T. Chien","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"R. Chien","raw_affiliation_strings":["Coordinated Science Laboratory, University of Illinois, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066350395","display_name":"Chao-Kai Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chao-Kai Liu","raw_affiliation_strings":["Bell Telephone Laboratories, Inc., Holmdel, NJ, USA","Coordinated Science Laboratory, University of Illinois, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Telephone Laboratories, Inc., Holmdel, NJ, USA","institution_ids":[]},{"raw_affiliation_string":"Coordinated Science Laboratory, University of Illinois, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.16011888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"19","issue":"5","first_page":"678","last_page":"682"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9969000220298767,"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"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9947999715805054,"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/arithmetic","display_name":"Arithmetic","score":0.6763564944267273},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6014564037322998},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5903334617614746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.576208770275116},{"id":"https://openalex.org/keywords/luby-transform-code","display_name":"Luby transform code","score":0.46485769748687744},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.451229453086853},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.44927841424942017},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4281836748123169},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.36475348472595215},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3405972123146057},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.29451847076416016}],"concepts":[{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6763564944267273},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6014564037322998},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5903334617614746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.576208770275116},{"id":"https://openalex.org/C128151799","wikidata":"https://www.wikidata.org/wiki/Q13563306","display_name":"Luby transform code","level":5,"score":0.46485769748687744},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.451229453086853},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.44927841424942017},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4281836748123169},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.36475348472595215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3405972123146057},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.29451847076416016},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1973.1055086","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1973.1055086","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1594652978","https://openalex.org/W1888253881","https://openalex.org/W1964329692","https://openalex.org/W2064759901","https://openalex.org/W2098134883","https://openalex.org/W2143160443","https://openalex.org/W2161506283","https://openalex.org/W2166676953","https://openalex.org/W2334439626","https://openalex.org/W2590257241","https://openalex.org/W4234345682"],"related_works":["https://openalex.org/W2460434904","https://openalex.org/W4246934899","https://openalex.org/W2113911300","https://openalex.org/W4383466497","https://openalex.org/W4205600360","https://openalex.org/W2156895811","https://openalex.org/W2095450438","https://openalex.org/W1992135520","https://openalex.org/W2293846540","https://openalex.org/W4287025061"],"abstract_inverted_index":{"A":[0,20],"new":[1,32,40],"class":[2,33,41,67],"of":[3,14,34,42,68],"cyclic":[4],"multiple-error-correcting":[5],"arithmetic":[6,29,43],"codes":[7,16,35,44],"is":[8,17,25,36,62],"described,":[9],"and":[10,53],"the":[11,51,65],"minimum":[12],"distance":[13],"these":[15,28],"determined":[18],"analytically.":[19],"two-step":[21],"majority-logic":[22,59],"decoding":[23,60],"scheme":[24,61],"developed":[26,63],"for":[27,64],"codes.":[30,69],"The":[31],"extended":[37,66],"to":[38],"a":[39,46],"having":[45],"primitive":[47],"cyclotomic":[48],"factor":[49],"as":[50],"generator":[52],"an":[54],"<tex":[55],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[56],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">L</tex>":[57],"-step":[58]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
