{"id":"https://openalex.org/W2141094714","doi":"https://doi.org/10.1109/tit.2011.2144955","title":"On the Size of Optimal Three-Error-Correcting Binary Codes of Length 16","display_name":"On the Size of Optimal Three-Error-Correcting Binary Codes of Length 16","publication_year":2011,"publication_date":"2011-10-01","ids":{"openalex":"https://openalex.org/W2141094714","doi":"https://doi.org/10.1109/tit.2011.2144955","mag":"2141094714"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2011.2144955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2144955","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/A5009643905","display_name":"Patric R. J. \u00d6sterg\u00e5rd","orcid":"https://orcid.org/0000-0003-0426-9771"},"institutions":[{"id":"https://openalex.org/I9927081","display_name":"Aalto University","ror":"https://ror.org/020hwjq30","country_code":"FI","type":"education","lineage":["https://openalex.org/I9927081"]}],"countries":["FI"],"is_corresponding":true,"raw_author_name":"Patric R. J. Ostergard","raw_affiliation_strings":["Department of Communications and Networking, School of Electrical Engineering, Aalto University, Aalto, Finland","Department of Communications and Networking, Aalto University, Aalto, Finland#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Communications and Networking, School of Electrical Engineering, Aalto University, Aalto, Finland","institution_ids":["https://openalex.org/I9927081"]},{"raw_affiliation_string":"Department of Communications and Networking, Aalto University, Aalto, Finland#TAB#","institution_ids":["https://openalex.org/I9927081"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5009643905"],"corresponding_institution_ids":["https://openalex.org/I9927081"],"apc_list":null,"apc_paid":null,"fwci":0.4276,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.7380519,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"57","issue":"10","first_page":"6824","last_page":"6826"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9994999766349792,"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":0.9994999766349792,"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":0.9991999864578247,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.6210788488388062},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4678794741630554},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44379955530166626},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.37100154161453247},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35862216353416443},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3388296365737915},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32179564237594604},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.12049761414527893},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.10184517502784729}],"concepts":[{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.6210788488388062},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4678794741630554},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44379955530166626},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.37100154161453247},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35862216353416443},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3388296365737915},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32179564237594604},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.12049761414527893},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.10184517502784729},{"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.2011.2144955","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2011.2144955","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":13,"referenced_works":["https://openalex.org/W1602929565","https://openalex.org/W1606480398","https://openalex.org/W2020623695","https://openalex.org/W2022962668","https://openalex.org/W2041588219","https://openalex.org/W2100838727","https://openalex.org/W2126542268","https://openalex.org/W2137806147","https://openalex.org/W2154746932","https://openalex.org/W2168946262","https://openalex.org/W2739148627","https://openalex.org/W3123893438","https://openalex.org/W4292408570"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2317200988","https://openalex.org/W2052122378","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2980963558","https://openalex.org/W2181413294"],"abstract_inverted_index":{"Let":[0],"<i":[1,5,9,23,29,40,45],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,6,10,24,30,41,46],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">A</i>":[3,42,47],"(":[4],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">n</i>":[7,25],",":[8],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">d</i>":[11,31],")":[12],"denote":[13],"the":[14,56,82,89],"maximum":[15],"size":[16,57,90],"of":[17,58,63,91],"a":[18,72,78],"binary":[19,61],"code":[20],"with":[21],"length":[22,64],"and":[26,77],"minimum":[27],"distance":[28],".":[32],"It":[33],"has":[34],"been":[35],"known":[36],"for":[37],"decades":[38],"that":[39,53,55,88],"(16,7)":[43],"=":[44,49],"(17,8)":[48],"36":[50,68],"or":[51,69],"37,":[52],"is,":[54],"optimal":[59,92],"3-error-correcting":[60],"codes":[62,94],"16":[65],"is":[66,86,95],"either":[67],"37.":[70],"By":[71],"recursive":[73],"classification":[74],"via":[75],"subcodes":[76],"clique":[79],"search":[80],"in":[81],"final":[83],"stage,":[84],"it":[85],"shown":[87],"such":[93],"36.":[96]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}