{"id":"https://openalex.org/W2102520548","doi":"https://doi.org/10.1109/tit.1969.1054261","title":"New binary coding results by circulants","display_name":"New binary coding results by circulants","publication_year":1969,"publication_date":"1969-01-01","ids":{"openalex":"https://openalex.org/W2102520548","doi":"https://doi.org/10.1109/tit.1969.1054261","mag":"2102520548"},"language":"en","primary_location":{"id":"doi:10.1109/tit.1969.1054261","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054261","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/A5023839418","display_name":"M. Karlin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"M. Karlin","raw_affiliation_strings":["M. B. L. E., Brussels, Belgium","[M. B. L. E., Brussels, Belgium]"],"affiliations":[{"raw_affiliation_string":"M. B. L. E., Brussels, Belgium","institution_ids":[]},{"raw_affiliation_string":"[M. B. L. E., Brussels, Belgium]","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023839418"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.5977,"has_fulltext":false,"cited_by_count":137,"citation_normalized_percentile":{"value":0.96919243,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"15","issue":"1","first_page":"81","last_page":"92"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9987999796867371,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9975000023841858,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.5106509327888489},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.46342766284942627},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.44472843408584595},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.416730135679245},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4111676812171936},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3956298232078552},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3681514263153076},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18572798371315002},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.11723348498344421}],"concepts":[{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.5106509327888489},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.46342766284942627},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.44472843408584595},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.416730135679245},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4111676812171936},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3956298232078552},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3681514263153076},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18572798371315002},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.11723348498344421},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.1969.1054261","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.1969.1054261","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":15,"referenced_works":["https://openalex.org/W1979203027","https://openalex.org/W1995229050","https://openalex.org/W2005582075","https://openalex.org/W2019109963","https://openalex.org/W2048731540","https://openalex.org/W2053184624","https://openalex.org/W2064759901","https://openalex.org/W2068933160","https://openalex.org/W2076597612","https://openalex.org/W2104687090","https://openalex.org/W2108730615","https://openalex.org/W2144253890","https://openalex.org/W2294436629","https://openalex.org/W2322463333","https://openalex.org/W3175367423"],"related_works":["https://openalex.org/W2139378013","https://openalex.org/W2560470131","https://openalex.org/W2049656902","https://openalex.org/W2394404719","https://openalex.org/W2903415888","https://openalex.org/W4287113494","https://openalex.org/W2348308003","https://openalex.org/W3148564979","https://openalex.org/W2063363084","https://openalex.org/W2964130583"],"abstract_inverted_index":{"The":[0,84],"Introduction":[1],"contains":[2],"a":[3,39,59,145],"new":[4,86],"circulant":[5,32,170],"echelon":[6],"canonical":[7],"form":[8,63],"for":[9,120],"the":[10,29,49,56,62,93,151,159],"perfect":[11],"<tex":[12,34,64,94,99,121,160],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[13,35,65,95,100,122,161],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(23,12)</tex>":[14],"Golay":[15],"code":[16],"and":[17,38,119,168],"some":[18,143],"tentative":[19],"conclusions":[20],"are":[21,79,90,136,172],"suggested.":[22],"Section":[23,69,130],"I":[24],"gives":[25],"an":[26],"account":[27],"of":[28,31,41,52,58,61,81,140,166],"properties":[30],"matrices":[33],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</tex>":[36],",":[37],"number":[40],"lemmas":[42],"that":[43,74],"make":[44],"it":[45,71],"possible":[46],"to":[47],"determine":[48],"minimum":[50,87],"weight":[51,88],"codes":[53,78,135,157,171],"generated":[54],"by":[55,138],"rows":[57],"matrix":[60],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">|E|A|</tex>":[66],".":[67,128],"In":[68,129,142],"II,":[70],"is":[72,148],"shown":[73],"many":[75],"quadratic":[76],"residue":[77],"almost":[80],"this":[82],"form.":[83],"following":[85],"results":[89],"obtained:":[91],"For":[92],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(79,":[96],"40)</tex>":[97],"code,":[98],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">w":[101],"=":[102,107,112,117,126],"15;":[103],"(103,":[104],"52),":[105],"w":[106,111,116,125],"19;":[108,113],"(151,":[109],"76),":[110],"(89,":[114],"45),":[115],"17</tex>":[118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(113,":[123],"57),":[124],"15</tex>":[127],"III,":[131],"high-quality":[132],"(noncyclic)":[133],"group":[134],"constructed":[137],"means":[139],"circulants.":[141],"cases":[144],"definite":[146],"improvement":[147],"obtained":[149],"on":[150],"best":[152],"previously":[153],"known":[154],"Bose-Chaudhuri-Hocquenghem":[155],"cyclic":[156],"(including":[158],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">(31,":[162],"16)</tex>":[163],"code).":[164],"Methods":[165],"coding":[167],"decoding":[169],"not":[173],"discussed.":[174]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}