{"id":"https://openalex.org/W2957040986","doi":"https://doi.org/10.1109/tit.2021.3113367","title":"Entanglement-Assisted Quantum Codes From Algebraic Geometry Codes","display_name":"Entanglement-Assisted Quantum Codes From Algebraic Geometry Codes","publication_year":2021,"publication_date":"2021-09-16","ids":{"openalex":"https://openalex.org/W2957040986","doi":"https://doi.org/10.1109/tit.2021.3113367","mag":"2957040986"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2021.3113367","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3113367","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1907.06357","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030605260","display_name":"Francisco Revson F. Pereira","orcid":"https://orcid.org/0000-0001-5638-6334"},"institutions":[{"id":"https://openalex.org/I41455075","display_name":"Universidade Federal de Campina Grande","ror":"https://ror.org/00eftnx64","country_code":"BR","type":"education","lineage":["https://openalex.org/I41455075"]},{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["BR","NL"],"is_corresponding":false,"raw_author_name":"Francisco Revson F. Pereira","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil","Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, AZ, The Netherlands","[Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil]"],"raw_orcid":"https://orcid.org/0000-0001-5638-6334","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil","institution_ids":["https://openalex.org/I41455075"]},{"raw_affiliation_string":"Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, AZ, The Netherlands","institution_ids":["https://openalex.org/I83019370"]},{"raw_affiliation_string":"[Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil]","institution_ids":["https://openalex.org/I41455075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073459171","display_name":"Ruud Pellikaan","orcid":"https://orcid.org/0000-0002-9547-3657"},"institutions":[{"id":"https://openalex.org/I83019370","display_name":"Eindhoven University of Technology","ror":"https://ror.org/02c2kyt77","country_code":"NL","type":"education","lineage":["https://openalex.org/I83019370"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Ruud Pellikaan","raw_affiliation_strings":["Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, AZ, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computing Science, Eindhoven University of Technology, Eindhoven, AZ, The Netherlands","institution_ids":["https://openalex.org/I83019370"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028337242","display_name":"Giuliano G. La Guardia","orcid":"https://orcid.org/0000-0002-0205-9597"},"institutions":[{"id":"https://openalex.org/I68207295","display_name":"Universidade Estadual de Ponta Grossa","ror":"https://ror.org/027s08w94","country_code":"BR","type":"education","lineage":["https://openalex.org/I68207295"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Giuliano Gadioli La Guardia","raw_affiliation_strings":["Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG), Ponta Grossa, Brazil","Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG) , Ponta Grossa, Brazil"],"raw_orcid":"https://orcid.org/0000-0002-0205-9597","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG), Ponta Grossa, Brazil","institution_ids":["https://openalex.org/I68207295"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, State University of Ponta Grossa (UEPG) , Ponta Grossa, Brazil","institution_ids":["https://openalex.org/I68207295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058758241","display_name":"Francisco de Assis","orcid":"https://orcid.org/0000-0002-8619-0874"},"institutions":[{"id":"https://openalex.org/I41455075","display_name":"Universidade Federal de Campina Grande","ror":"https://ror.org/00eftnx64","country_code":"BR","type":"education","lineage":["https://openalex.org/I41455075"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Francisco Marcos de Assis","raw_affiliation_strings":["Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil","[Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil","institution_ids":["https://openalex.org/I41455075"]},{"raw_affiliation_string":"[Department of Electrical Engineering, Federal University of Campina Grande (UFCG), Campina Grande, Brazil]","institution_ids":["https://openalex.org/I41455075"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":0.4204,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69012782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"67","issue":"11","first_page":"7110","last_page":"7120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":1.0,"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/T11130","display_name":"Coding theory and cryptography","score":0.9990000128746033,"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/T13182","display_name":"Quantum-Dot Cellular Automata","score":0.9973999857902527,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quantum-convolutional-code","display_name":"Quantum convolutional code","score":0.72076416015625},{"id":"https://openalex.org/keywords/quantum-entanglement","display_name":"Quantum entanglement","score":0.51966392993927},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.5057988166809082},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5036224722862244},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.4777771234512329},{"id":"https://openalex.org/keywords/tornado-code","display_name":"Tornado code","score":0.45222997665405273},{"id":"https://openalex.org/keywords/decoherence-free-subspaces","display_name":"Decoherence-free subspaces","score":0.45052793622016907},{"id":"https://openalex.org/keywords/quantum-error-correction","display_name":"Quantum error correction","score":0.42292889952659607},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39845284819602966},{"id":"https://openalex.org/keywords/quantum-information","display_name":"Quantum information","score":0.3654215335845947},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.32163146138191223},{"id":"https://openalex.org/keywords/quantum","display_name":"Quantum","score":0.30000707507133484},{"id":"https://openalex.org/keywords/quantum-channel","display_name":"Quantum channel","score":0.2735442519187927},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24701321125030518},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.23029744625091553},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.08656111359596252}],"concepts":[{"id":"https://openalex.org/C69497775","wikidata":"https://www.wikidata.org/wiki/Q7269025","display_name":"Quantum convolutional code","level":5,"score":0.72076416015625},{"id":"https://openalex.org/C121040770","wikidata":"https://www.wikidata.org/wiki/Q215675","display_name":"Quantum entanglement","level":3,"score":0.51966392993927},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.5057988166809082},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5036224722862244},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.4777771234512329},{"id":"https://openalex.org/C65058987","wikidata":"https://www.wikidata.org/wiki/Q7826005","display_name":"Tornado code","level":5,"score":0.45222997665405273},{"id":"https://openalex.org/C191608238","wikidata":"https://www.wikidata.org/wiki/Q5249552","display_name":"Decoherence-free subspaces","level":5,"score":0.45052793622016907},{"id":"https://openalex.org/C51003876","wikidata":"https://www.wikidata.org/wiki/Q1536431","display_name":"Quantum error correction","level":4,"score":0.42292889952659607},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39845284819602966},{"id":"https://openalex.org/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.3654215335845947},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.32163146138191223},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.30000707507133484},{"id":"https://openalex.org/C187486625","wikidata":"https://www.wikidata.org/wiki/Q2122176","display_name":"Quantum channel","level":4,"score":0.2735442519187927},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24701321125030518},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.23029744625091553},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.08656111359596252}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1109/tit.2021.3113367","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2021.3113367","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"},{"id":"pmh:oai:pure.tue.nl:openaire_cris_publications/288c1ae6-d39a-4a8b-ae77-013af2355dc0","is_oa":false,"landing_page_url":"https://research.tue.nl/en/publications/288c1ae6-d39a-4a8b-ae77-013af2355dc0","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pereira, F R F, Pellikaan, R, La Guardia, G G & de Assis, F M 2021, 'Entanglement-Assisted Quantum Codes from Algebraic Geometry Codes', IEEE Transactions on Information Theory, vol. 67, no. 11, pp. 7110-7120. https://doi.org/10.1109/TIT.2021.3113367","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:arXiv.org:1907.06357","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.06357","pdf_url":"https://arxiv.org/pdf/1907.06357","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:tue:oai:pure.tue.nl:publications/daf697d0-7b11-4b0a-b372-fe242e5705ac","is_oa":true,"landing_page_url":"https://research.tue.nl/nl/publications/daf697d0-7b11-4b0a-b372-fe242e5705ac","pdf_url":"https://research.tue.nl/nl/publications/daf697d0-7b11-4b0a-b372-fe242e5705ac","source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv, 2019:1907.06357v1. Cornell University Library","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2957040986","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1907.06357","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:pure.tue.nl:openaire/daf697d0-7b11-4b0a-b372-fe242e5705ac","is_oa":true,"landing_page_url":"https://research.tue.nl/en/publications/daf697d0-7b11-4b0a-b372-fe242e5705ac","pdf_url":null,"source":{"id":"https://openalex.org/S4406922641","display_name":"TU/e Research Portal","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fernandes Pereira, F, Pellikaan, R, Gadioli La Guardia, G & de Assis, F M 2019, 'Entanglement-assisted quantum codes from algebraic geometry codes', arXiv, vol. 2019, 1907.06357v1. https://doi.org/10.48550/arXiv.1907.06357","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1907.06357","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1907.06357","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1907.06357","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1907.06357","pdf_url":"https://arxiv.org/pdf/1907.06357","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":[{"id":"https://openalex.org/G8930538054","display_name":null,"funder_award_id":"201223/2018-0","funder_id":"https://openalex.org/F4320322025","funder_display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico"}],"funders":[{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":45,"referenced_works":["https://openalex.org/W15967873","https://openalex.org/W1557415002","https://openalex.org/W1559343931","https://openalex.org/W1585138385","https://openalex.org/W1613141042","https://openalex.org/W1631356911","https://openalex.org/W1975135614","https://openalex.org/W1982432882","https://openalex.org/W2002923615","https://openalex.org/W2003032902","https://openalex.org/W2003177806","https://openalex.org/W2020636832","https://openalex.org/W2040653896","https://openalex.org/W2051471360","https://openalex.org/W2055087798","https://openalex.org/W2062884415","https://openalex.org/W2089508405","https://openalex.org/W2111937453","https://openalex.org/W2128718974","https://openalex.org/W2143438504","https://openalex.org/W2162938940","https://openalex.org/W2255659056","https://openalex.org/W2296577438","https://openalex.org/W2594351374","https://openalex.org/W2891802825","https://openalex.org/W2891992737","https://openalex.org/W2905157741","https://openalex.org/W2963105100","https://openalex.org/W2963637464","https://openalex.org/W2963803325","https://openalex.org/W2963992280","https://openalex.org/W2971236079","https://openalex.org/W3033331243","https://openalex.org/W3098999158","https://openalex.org/W3102640842","https://openalex.org/W3121556672","https://openalex.org/W3144380511","https://openalex.org/W4206775542","https://openalex.org/W4301287831","https://openalex.org/W6600658134","https://openalex.org/W6631987434","https://openalex.org/W6634977691","https://openalex.org/W6693001733","https://openalex.org/W6697183508","https://openalex.org/W6754714785"],"related_works":["https://openalex.org/W3200987404","https://openalex.org/W3149150466","https://openalex.org/W3084777614","https://openalex.org/W3102640842","https://openalex.org/W2952508172","https://openalex.org/W1915062826","https://openalex.org/W1976213622","https://openalex.org/W2983818199","https://openalex.org/W2952077290","https://openalex.org/W3102121229","https://openalex.org/W3088266360","https://openalex.org/W3104330661","https://openalex.org/W1839785972","https://openalex.org/W2785335201","https://openalex.org/W3006031636","https://openalex.org/W3107395148","https://openalex.org/W2266100521","https://openalex.org/W3163495057","https://openalex.org/W2782792299","https://openalex.org/W2963105100"],"abstract_inverted_index":{"Quantum":[0],"error-correcting":[1,38,61],"codes":[2,39,56,71,78,93,111,129,139,169],"play":[3],"the":[4,24,45,51,81,84,117,148,156],"role":[5],"of":[6,26,50,76,92,109,125,137,167],"suppressing":[7],"noise":[8],"and":[9,83],"decoherence":[10],"in":[11],"quantum":[12,37,60,95,118,149],"systems":[13],"by":[14,48,154],"introducing":[15],"redundancy.":[16],"Some":[17],"strategies":[18],"can":[19,32],"be":[20],"used":[21,131],"to":[22,40,72,100,132,162],"improve":[23],"parameters":[25],"these":[27],"codes.":[28,63],"For":[29],"example,":[30],"entanglement":[31],"provide":[33],"a":[34,144],"way":[35],"for":[36],"achieve":[41],"higher":[42],"rates":[43],"than":[44],"one":[46],"obtained":[47],"means":[49],"traditional":[52],"stabilizer":[53],"formalism.":[54],"Such":[55],"are":[57,130],"called":[58],"entanglement-assisted":[59],"(EAQEC)":[62],"In":[64],"this":[65,172],"paper,":[66],"we":[67],"utilize":[68],"algebraic":[69],"geometry":[70],"construct":[73,107],"several":[74],"families":[75,88,108,136],"EAQEC":[77,110,138,168],"derived":[79],"from":[80],"Euclidean":[82],"Hermitian":[85],"construction.":[86],"Three":[87],"constructed":[89],"here":[90],"consist":[91],"whose":[94],"Singleton":[96],"defect":[97],"is":[98,160],"equal":[99],"zero,":[101],"one,":[102],"or":[103],"two.":[104],"We":[105],"also":[106],"with":[112,147],"an":[113,164],"encoding":[114],"rate":[115],"exceeding":[116],"Gilbert-Varshamov":[119,150],"bound.":[120,173],"Additionally,":[121],"asymptotically":[122,134,165],"good":[123,135],"towers":[124],"linear":[126],"complementary":[127],"dual":[128],"obtain":[133],"consuming":[140],"maximal":[141],"entanglement.":[142],"Furthermore,":[143],"simple":[145],"comparison":[146],"bound":[151],"demonstrates":[152],"that,":[153],"utilizing":[155],"proposed":[157],"construction,":[158],"it":[159],"possible":[161],"generate":[163],"family":[166],"that":[170],"exceeds":[171]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2019-07-23T00:00:00"}
