{"id":"https://openalex.org/W3149455038","doi":"https://doi.org/10.1109/tit.1959.1057538","title":"Group code equivalence and optimum codes","display_name":"Group code equivalence and optimum codes","publication_year":1959,"publication_date":"1959-05-01","ids":{"openalex":"https://openalex.org/W3149455038","doi":"https://doi.org/10.1109/tit.1959.1057538","mag":"3149455038"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1959.1057538","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1959.1057538","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/A5085255309","display_name":"Alain Fontaine","orcid":null},"institutions":[{"id":"https://openalex.org/I1341412227","display_name":"IBM (United States)","ror":"https://ror.org/05hh8d621","country_code":"US","type":"company","lineage":["https://openalex.org/I1341412227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"A. Fontaine","raw_affiliation_strings":["Research Center, International Business Machines Corporation, Yorktown Heights, NY, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Center, International Business Machines Corporation, Yorktown Heights, NY, USA","institution_ids":["https://openalex.org/I1341412227"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021754157","display_name":"W. W. Peterson","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"W. Peterson","raw_affiliation_strings":["University of Florida, Gainesville, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.3542,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.97074756,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"5","issue":"5","first_page":"60","last_page":"70"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9950000047683716,"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":0.9950000047683716,"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":0.988099992275238,"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/T12162","display_name":"Cellular Automata and Applications","score":0.9839000105857849,"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/equivalence","display_name":"Equivalence (formal languages)","score":0.641372561454773},{"id":"https://openalex.org/keywords/group-code","display_name":"Group code","score":0.5714263319969177},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.5435691475868225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5372740030288696},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.51948082447052},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.4985027313232422},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4645659029483795},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.4607563614845276},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.45910999178886414},{"id":"https://openalex.org/keywords/raptor-code","display_name":"Raptor code","score":0.4577213525772095},{"id":"https://openalex.org/keywords/information-theory","display_name":"Information theory","score":0.44595977663993835},{"id":"https://openalex.org/keywords/turbo-code","display_name":"Turbo code","score":0.42763128876686096},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.41189101338386536},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.392974317073822},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.39287763833999634},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3527642488479614},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2587246894836426},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.22475209832191467},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.14015868306159973},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09778940677642822},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06977993249893188}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.641372561454773},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.5714263319969177},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.5435691475868225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5372740030288696},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.51948082447052},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.4985027313232422},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4645659029483795},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4607563614845276},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.45910999178886414},{"id":"https://openalex.org/C101252705","wikidata":"https://www.wikidata.org/wiki/Q7294373","display_name":"Raptor code","level":5,"score":0.4577213525772095},{"id":"https://openalex.org/C52622258","wikidata":"https://www.wikidata.org/wiki/Q131222","display_name":"Information theory","level":2,"score":0.44595977663993835},{"id":"https://openalex.org/C114504821","wikidata":"https://www.wikidata.org/wiki/Q2164281","display_name":"Turbo code","level":3,"score":0.42763128876686096},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.41189101338386536},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.392974317073822},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.39287763833999634},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3527642488479614},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2587246894836426},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.22475209832191467},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.14015868306159973},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09778940677642822},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06977993249893188},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1959.1057538","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1959.1057538","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W2121417875","https://openalex.org/W2165731899","https://openalex.org/W2521342193","https://openalex.org/W4239256076","https://openalex.org/W6820585419"],"related_works":["https://openalex.org/W2010277851","https://openalex.org/W2118665614","https://openalex.org/W2095450438","https://openalex.org/W1991401790","https://openalex.org/W2073982827","https://openalex.org/W2108753162","https://openalex.org/W2122691796","https://openalex.org/W2616450673","https://openalex.org/W2042187478","https://openalex.org/W3149455038"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3,45],"search":[4,26],"for":[5],"optimum":[6,39],"group":[7,54],"codes":[8,21,40],"using":[9],"the":[10,17,25,30],"IBM":[11],"704":[12],"computer.":[13],"Some":[14],"theory":[15],"of":[16,32,47],"relationship":[18],"between":[19],"equivalent":[20],"used":[22],"in":[23],"narrowing":[24],"is":[27,34],"described,":[28],"and":[29],"method":[31],"searching":[33],"outlined.":[35],"The":[36],"newly":[37],"found":[38],"are":[41],"listed,":[42],"along":[43],"with":[44],"number":[46],"counter-examples":[48],"to":[49],"typical":[50],"conjectures":[51],"on":[52],"binary":[53],"codes.":[55]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}