{"id":"https://openalex.org/W2485226336","doi":"https://doi.org/10.1109/isit.2016.7541515","title":"Rate-distance tradeoff for codes above graph capacity","display_name":"Rate-distance tradeoff for codes above graph capacity","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2485226336","doi":"https://doi.org/10.1109/isit.2016.7541515","mag":"2485226336"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541515","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.06384","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089243170","display_name":"Daniel Cullina","orcid":"https://orcid.org/0000-0002-7471-2102"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Daniel Cullina","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, United States","University of Illinois, Urbana-Champaign"],"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, United States","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois, Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037433671","display_name":"Marco Dalai","orcid":"https://orcid.org/0000-0003-2132-7072"},"institutions":[{"id":"https://openalex.org/I30667456","display_name":"Brescia University","ror":"https://ror.org/015ahgd08","country_code":"US","type":"education","lineage":["https://openalex.org/I30667456"]},{"id":"https://openalex.org/I79940851","display_name":"University of Brescia","ror":"https://ror.org/02q2d2610","country_code":"IT","type":"education","lineage":["https://openalex.org/I79940851"]}],"countries":["IT","US"],"is_corresponding":false,"raw_author_name":"Marco Dalai","raw_affiliation_strings":["University of Brescia, Italy","University of Brescia"],"affiliations":[{"raw_affiliation_string":"University of Brescia, Italy","institution_ids":["https://openalex.org/I79940851"]},{"raw_affiliation_string":"University of Brescia","institution_ids":["https://openalex.org/I30667456","https://openalex.org/I79940851"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031031216","display_name":"Yury Polyanskiy","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yury Polyanskiy","raw_affiliation_strings":["Massachusetts Institute of Technology, United States","Massachusetts Institute of Technology"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, United States","institution_ids":["https://openalex.org/I63966007"]},{"raw_affiliation_string":"Massachusetts Institute of Technology","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089243170"],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":0.1867,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.57479324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":null,"issue":null,"first_page":"1331","last_page":"1335"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994000196456909,"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/T11130","display_name":"Coding theory and cryptography","score":0.9994000196456909,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mceliece-cryptosystem","display_name":"McEliece cryptosystem","score":0.7530662417411804},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6815220713615417},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5833125114440918},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5356675386428833},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5122231841087341},{"id":"https://openalex.org/keywords/hamming-distance","display_name":"Hamming distance","score":0.48732075095176697},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.4607997238636017},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42817315459251404},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.42738085985183716},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4222761392593384},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4177819788455963},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2355041205883026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1950283944606781}],"concepts":[{"id":"https://openalex.org/C16935551","wikidata":"https://www.wikidata.org/wiki/Q1042583","display_name":"McEliece cryptosystem","level":4,"score":0.7530662417411804},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6815220713615417},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5833125114440918},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5356675386428833},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5122231841087341},{"id":"https://openalex.org/C193319292","wikidata":"https://www.wikidata.org/wiki/Q272172","display_name":"Hamming distance","level":2,"score":0.48732075095176697},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.4607997238636017},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42817315459251404},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.42738085985183716},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4222761392593384},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4177819788455963},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2355041205883026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1950283944606781},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.0},{"id":"https://openalex.org/C6295992","wikidata":"https://www.wikidata.org/wiki/Q976521","display_name":"Cryptosystem","level":3,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/isit.2016.7541515","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541515","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1607.06384","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.06384","pdf_url":"https://arxiv.org/pdf/1607.06384","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:dspace.mit.edu:1721.1/111670","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/111670","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv","raw_type":"http://purl.org/eprint/type/ConferencePaper"},{"id":"pmh:oai:iris.unibs.it:11379/486194","is_oa":false,"landing_page_url":"http://hdl.handle.net/11379/486194","pdf_url":null,"source":{"id":"https://openalex.org/S4306400804","display_name":"Institutional Research Information System (Universit\u00e0 degli Studi di Brescia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1607.06384","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.06384","pdf_url":"https://arxiv.org/pdf/1607.06384","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1479863711","https://openalex.org/W1988856559","https://openalex.org/W2003177806","https://openalex.org/W2019155885","https://openalex.org/W2034215849","https://openalex.org/W2078289947","https://openalex.org/W2088668281","https://openalex.org/W2109084006","https://openalex.org/W2114189119","https://openalex.org/W2118333520","https://openalex.org/W2164684058","https://openalex.org/W2501406367","https://openalex.org/W3104511676","https://openalex.org/W3141776272"],"related_works":["https://openalex.org/W1516862653","https://openalex.org/W4250694056","https://openalex.org/W2529734863","https://openalex.org/W2949842450","https://openalex.org/W2084291137","https://openalex.org/W3028851644","https://openalex.org/W2059211373","https://openalex.org/W2149636648","https://openalex.org/W641845919","https://openalex.org/W2100679162"],"abstract_inverted_index":{"The":[0,69],"capacity":[1],"of":[2,10,13,20,46,67,78,83,98,124,158],"a":[3,44,64,88,95,121],"graph":[4,118],"is":[5],"defined":[6],"as":[7,75],"the":[8,17,21,24,47,52,76,80,125,146,155],"rate":[9,82],"exponential":[11],"growth":[12],"independent":[14],"sets":[15],"in":[16,51,61,160],"strong":[18,25],"powers":[19],"graph.":[22],"In":[23],"power":[26,53],"an":[27,131],"edge":[28],"connects":[29],"two":[30],"sequences":[31,58],"if":[32],"at":[33],"each":[34],"position":[35],"their":[36],"letters":[37],"are":[38,55,107],"equal":[39],"or":[40],"adjacent.":[41],"We":[42,109,128],"consider":[43],"variation":[45],"problem":[48,77],"where":[49,93],"edges":[50],"graphs":[54],"removed":[56],"between":[57],"which":[59,140],"differ":[60],"more":[62],"than":[63],"fraction":[65,96],"\u03b4":[66,97],"coordinates.":[68],"proposed":[70],"generalization":[71,123],"can":[72,100],"be":[73,101],"interpreted":[74],"determining":[79],"highest":[81],"zero":[84],"undetected-error":[85],"communication":[86],"over":[87],"link":[89],"with":[90,120,145],"adversarial":[91],"noise,":[92],"only":[94,104],"symbols":[99],"perturbed":[102],"and":[103],"some":[105],"substitutions":[106],"allowed.":[108],"derive":[110],"lower":[111],"bounds":[112],"on":[113,135],"achievable":[114],"rates":[115],"by":[116,149],"combining":[117],"homomorphisms":[119],"graph-theoretic":[122],"Gilbert-Varshamov":[126],"bound.":[127],"then":[129],"give":[130],"upper":[132],"bound,":[133],"based":[134],"Delsarte's":[136],"linear":[137],"programming":[138],"approach,":[139],"combines":[141],"Lov\u00e1sz'":[142],"theta":[143],"function":[144],"construction":[147],"used":[148],"McEliece":[150],"et":[151],"al.":[152],"for":[153],"bounding":[154],"minimum":[156],"distance":[157],"codes":[159],"Hamming":[161],"spaces.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
