{"id":"https://openalex.org/W2752608965","doi":"https://doi.org/10.1007/s10623-018-0589-8","title":"Uniqueness of codes using semidefinite programming","display_name":"Uniqueness of codes using semidefinite programming","publication_year":2018,"publication_date":"2018-11-30","ids":{"openalex":"https://openalex.org/W2752608965","doi":"https://doi.org/10.1007/s10623-018-0589-8","mag":"2752608965","pmid":"https://pubmed.ncbi.nlm.nih.gov/31564772"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-018-0589-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-018-0589-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-018-0589-8.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-018-0589-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Andries E. Brouwer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andries E. Brouwer","raw_affiliation_strings":["Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amsterdam, The Netherlands","institution_ids":[]}]},{"author_position":"last","author":{"id":null,"display_name":"Sven C. Polak","orcid":null},"institutions":[{"id":"https://openalex.org/I865915315","display_name":"Vrije Universiteit Amsterdam","ror":"https://ror.org/008xxew50","country_code":"NL","type":"education","lineage":["https://openalex.org/I865915315"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Sven C. Polak","raw_affiliation_strings":["2Korteweg-De Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2Korteweg-De Vries Institute for Mathematics, University of Amsterdam, Amsterdam, The Netherlands","institution_ids":["https://openalex.org/I865915315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02686276,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"87","issue":"8","first_page":"1881","last_page":"1895"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.1826999932527542,"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"}},"topics":[{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.1826999932527542,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.1347000002861023,"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/T11797","display_name":"graph theory and CDMA systems","score":0.13279999792575836,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.7598000168800354},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6987000107765198},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.5644000172615051},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5446000099182129},{"id":"https://openalex.org/keywords/binary-code","display_name":"Binary code","score":0.49810001254081726},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4763000011444092},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.41429999470710754}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8575999736785889},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.7598000168800354},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6987000107765198},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.603600025177002},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.5644000172615051},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5446000099182129},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5412999987602234},{"id":"https://openalex.org/C63435697","wikidata":"https://www.wikidata.org/wiki/Q864135","display_name":"Binary code","level":3,"score":0.49810001254081726},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4763000011444092},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.41429999470710754},{"id":"https://openalex.org/C2778945305","wikidata":"https://www.wikidata.org/wiki/Q6865502","display_name":"Minimum weight","level":2,"score":0.4065999984741211},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4007999897003174},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.39239999651908875},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.33550000190734863},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.32829999923706055},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.29919999837875366},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.2630999982357025}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s10623-018-0589-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-018-0589-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-018-0589-8.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmid:31564772","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31564772","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, codes, and cryptography","raw_type":null},{"id":"pmh:oai:dare.uva.nl:openaire/41448090-ea5d-457c-9af3-ada00e4fb2c4","is_oa":true,"landing_page_url":"https://handle.uba.uva.nl/personal/pure/en/publications/uniqueness-of-codes-using-semidefinite-programming(41448090-ea5d-457c-9af3-ada00e4fb2c4).html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400088","display_name":"UvA-DARE (University of Amsterdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887064364","host_organization_name":"University of Amsterdam","host_organization_lineage":["https://openalex.org/I887064364"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Brouwer, A E & Polak, S C 2019, 'Uniqueness of codes using semidefinite programming', Designs, Codes and Cryptography, vol. 87, no. 8, pp. 1881-1895. https://doi.org/10.1007/s10623-018-0589-8","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1709.02195","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1709.02195","pdf_url":"https://arxiv.org/pdf/1709.02195","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"},{"id":"pmh:oai:cwi.nl:30365","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/30365","pdf_url":"https://ir.cwi.nl/pub/30365/30365.pdf","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes and Cryptography vol. 87, pp. 1881-1895","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:6743705","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6743705","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Des Codes Cryptogr","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s10623-018-0589-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-018-0589-8","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-018-0589-8.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1997210176","display_name":null,"funder_award_id":"339109","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2752608965.pdf","grobid_xml":"https://content.openalex.org/works/W2752608965.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1963661276","https://openalex.org/W1966360582","https://openalex.org/W1990600049","https://openalex.org/W2104385491","https://openalex.org/W2123109473","https://openalex.org/W2267943254","https://openalex.org/W2602721884"],"related_works":[],"abstract_inverted_index":{"For":[0],"$$n,d,w":[1],"\\in":[2],"\\mathbb":[3],"{N}$$":[4],",":[5,37],"let":[6],"A(n,":[7,58],"d,":[8],"w)":[9],"denote":[10,60],"the":[11,39,52,61],"maximum":[12,62],"size":[13,63],"of":[14,18,51,64,68],"a":[15,65],"binary":[16,66],"code":[17,67],"word":[19,69],"length":[20,70],"n,":[21],"minimum":[22,73],"distance":[23,74],"d":[24],"and":[25,38,44,72,94],"constant":[26],"weight":[27],"w.":[28],"Schrijver":[29],"recently":[30],"showed":[31,79],"using":[32],"semidefinite":[33],"programming":[34],"that":[35,42,80,85],"$$A(23,8,11)=1288$$":[36],"second":[40],"author":[41],"$$A(22,8,11)=672$$":[43],"$$A(22,8,10)=616$$":[45],".":[46,82],"Here":[47],"we":[48],"show":[49,84],"uniqueness":[50],"codes":[53,90,98],"achieving":[54,91],"these":[55],"bounds.":[56],"Let":[57],"d)":[59],"n":[71],"d.":[75],"Gijswijt":[76],"et":[77],"al.":[78],"$$A(20,8)=256$$":[81],"We":[83],"there":[86],"are":[87],"several":[88],"nonisomorphic":[89],"this":[92],"bound,":[93],"classify":[95],"all":[96,100],"such":[97],"with":[99],"distances":[101],"divisible":[102],"by":[103],"4.":[104]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2017-09-15T00:00:00"}
