{"id":"https://openalex.org/W1875517895","doi":"https://doi.org/10.3934/amc.2016013","title":"Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code","display_name":"Non-existence of a ternary constant weight $(16,5,15;2048)$ diameter perfect code","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W1875517895","doi":"https://doi.org/10.3934/amc.2016013","mag":"1875517895"},"language":"en","primary_location":{"id":"doi:10.3934/amc.2016013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016013","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=c3b295ca-dd4e-4bd9-a527-58c82be699e5","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=c3b295ca-dd4e-4bd9-a527-58c82be699e5","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Denis S. Krotov","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Denis S. Krotov","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Patric R. J. \u007f \u00d6sterg\u00e5rd","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patric R. J. \u007f \u00d6sterg\u00e5rd","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Olli Pottonen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olli Pottonen","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"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":2,"citation_normalized_percentile":{"value":0.00059753,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"2","first_page":"393","last_page":"399"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9150000214576721,"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"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9150000214576721,"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/T11130","display_name":"Coding theory and cryptography","score":0.06809999793767929,"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/T10849","display_name":"Finite Group Theory Research","score":0.00800000037997961,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ternary-operation","display_name":"Ternary operation","score":0.76910001039505},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6815999746322632},{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6438000202178955},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.503600001335144},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4634000062942505},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.4147000014781952},{"id":"https://openalex.org/keywords/minimum-weight","display_name":"Minimum weight","score":0.40560001134872437}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.942300021648407},{"id":"https://openalex.org/C64452783","wikidata":"https://www.wikidata.org/wiki/Q1524945","display_name":"Ternary operation","level":2,"score":0.76910001039505},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6815999746322632},{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6438000202178955},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.633899986743927},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.503600001335144},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4634000062942505},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4560000002384186},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4147000014781952},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.35440000891685486},{"id":"https://openalex.org/C166530166","wikidata":"https://www.wikidata.org/wiki/Q1970635","display_name":"Hamming bound","level":5,"score":0.34599998593330383},{"id":"https://openalex.org/C108906091","wikidata":"https://www.wikidata.org/wiki/Q7702927","display_name":"Ternary Golay code","level":5,"score":0.3343999981880188},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.3330000042915344},{"id":"https://openalex.org/C197242373","wikidata":"https://www.wikidata.org/wiki/Q5163613","display_name":"Constant-weight code","level":5,"score":0.32330000400543213},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2946999967098236},{"id":"https://openalex.org/C73150493","wikidata":"https://www.wikidata.org/wiki/Q853922","display_name":"Hamming code","level":4,"score":0.2615000009536743},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.25209999084472656}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/amc.2016013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016013","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=c3b295ca-dd4e-4bd9-a527-58c82be699e5","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1408.6927","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1408.6927","pdf_url":"https://arxiv.org/pdf/1408.6927","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.3934/amc.2016013","is_oa":true,"landing_page_url":"https://doi.org/10.3934/amc.2016013","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=c3b295ca-dd4e-4bd9-a527-58c82be699e5","source":{"id":"https://openalex.org/S161492159","display_name":"Advances in Mathematics of Communications","issn_l":"1930-5338","issn":["1930-5338","1930-5346"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Mathematics of Communications","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1875517895.pdf","grobid_xml":"https://content.openalex.org/works/W1875517895.grobid-xml"},"referenced_works_count":12,"referenced_works":["https://openalex.org/W165726963","https://openalex.org/W1539721799","https://openalex.org/W1557392949","https://openalex.org/W1573473661","https://openalex.org/W1584248758","https://openalex.org/W1987233725","https://openalex.org/W2061471916","https://openalex.org/W2078373572","https://openalex.org/W2081069310","https://openalex.org/W2118297173","https://openalex.org/W4248135912","https://openalex.org/W6740226753"],"related_works":[],"abstract_inverted_index":{"Ternary":[0],"constant":[1],"weight":[2,7],"codes":[3,46,52],"of":[4,26,44],"length":[5],"$n=2^m$,":[6],"$n-1$,cardinality":[8],"$2^n$":[9],"and":[10,38],"distance":[11],"$5$":[12],"are":[13],"known":[14],"to":[15],"existfor":[16],"every":[17],"$m$":[18],"for":[19,32,39,47],"which":[20],"there":[21],"exists":[22],"an":[23],"APN":[24],"permutation":[25],"order":[27],"$2^m$,that":[28],"is,":[29],"at":[30],"least":[31],"all":[33],"odd":[34],"$m":[35],"\\geq":[36],"3$":[37],"$m=6$.We":[40],"show":[41],"the":[42,54],"non-existence":[43],"such":[45],"$m=4$and":[48],"prove":[49],"that":[50],"any":[51],"with":[53],"parameters":[55],"above":[56],"arediameter":[57],"perfect.":[58]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2016-06-24T00:00:00"}