{"id":"https://openalex.org/W4402218236","doi":"https://doi.org/10.1109/tit.2024.3454480","title":"Stabilizer Codes Over Fields of Even Order","display_name":"Stabilizer Codes Over Fields of Even Order","publication_year":2024,"publication_date":"2024-09-04","ids":{"openalex":"https://openalex.org/W4402218236","doi":"https://doi.org/10.1109/tit.2024.3454480"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2024.3454480","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3454480","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":true,"oa_status":"green","oa_url":"https://upcommons.upc.edu/bitstreams/47ef2914-4074-49cc-a562-d7e7ff04db83/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040387138","display_name":"Simeon Ball","orcid":"https://orcid.org/0000-0003-4845-2084"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Simeon Ball","raw_affiliation_strings":["Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, C. Pau Gargallo 14, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, C. Pau Gargallo 14, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111112544","display_name":"Edgar Moreno","orcid":null},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Edgar Moreno","raw_affiliation_strings":["Higher Interdisciplinary Training Center (CFIS), Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","Higher Interdisciplinary Training Center (CFIS), Universitat Polit&#x00E8;cnica de Catalunya, C. Pau Gargallo 14, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Higher Interdisciplinary Training Center (CFIS), Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Higher Interdisciplinary Training Center (CFIS), Universitat Polit&#x00E8;cnica de Catalunya, C. Pau Gargallo 14, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069446671","display_name":"Robin Simoens","orcid":"https://orcid.org/0000-0001-7398-3085"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Robin Simoens","raw_affiliation_strings":["Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, C. Pau Gargallo 14, Barcelona, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]},{"raw_affiliation_string":"Department of Mathematics, Universitat Polit&#x00E8;cnica de Catalunya, C. Pau Gargallo 14, Barcelona, Spain","institution_ids":["https://openalex.org/I9617848"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040387138"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12336975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"71","issue":"5","first_page":"3707","last_page":"3718"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9817000031471252,"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/T11321","display_name":"Error Correcting Code Techniques","score":0.9433000087738037,"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/stabiliser","display_name":"Stabiliser","score":0.545491635799408},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5247809290885925},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45498740673065186},{"id":"https://openalex.org/keywords/business","display_name":"Business","score":0.1228857934474945},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.0909300148487091}],"concepts":[{"id":"https://openalex.org/C2780345374","wikidata":"https://www.wikidata.org/wiki/Q7595716","display_name":"Stabiliser","level":2,"score":0.545491635799408},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5247809290885925},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45498740673065186},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.1228857934474945},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0909300148487091},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C31903555","wikidata":"https://www.wikidata.org/wiki/Q1637030","display_name":"Food science","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tit.2024.3454480","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2024.3454480","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:upcommons.upc.edu:2117/428482","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/428482","pdf_url":"https://upcommons.upc.edu/bitstreams/47ef2914-4074-49cc-a562-d7e7ff04db83/download","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:archive.ugent.be:01JN3NZQZ1XQZE39CG6HXTPPPG","is_oa":true,"landing_page_url":"http://hdl.handle.net/1854/LU-01JN3NZQZ1XQZE39CG6HXTPPPG","pdf_url":"https://biblio.ugent.be/publication/01JN3NZQZ1XQZE39CG6HXTPPPG/file/01JR0GEPQB9A934JXH18G14ZC0.pdf","source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"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":"ISSN: 1557-9654","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:upcommons.upc.edu:2117/428482","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/428482","pdf_url":"https://upcommons.upc.edu/bitstreams/47ef2914-4074-49cc-a562-d7e7ff04db83/download","source":{"id":"https://openalex.org/S4377196262","display_name":"UPCommons institutional repository (Universitat Polit\u00e8cnica de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I9617848","host_organization_name":"Universitat Polit\u00e8cnica de Catalunya","host_organization_lineage":["https://openalex.org/I9617848"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1419670400","display_name":null,"funder_award_id":"GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G1650125035","display_name":null,"funder_award_id":"B-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G2262748287","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3429648993","display_name":null,"funder_award_id":"PID202","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G3480869486","display_name":null,"funder_award_id":"13039","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4126322094","display_name":null,"funder_award_id":"01100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G4538077655","display_name":null,"funder_award_id":"PID2020-113082GB-I00","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5388806002","display_name":null,"funder_award_id":"unknown","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G5421974903","display_name":null,"funder_award_id":"501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G5805502524","display_name":null,"funder_award_id":"PID2020","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G6589649124","display_name":null,"funder_award_id":"PID2020-","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G661330594","display_name":null,"funder_award_id":"00110","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G6685425346","display_name":null,"funder_award_id":"0011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G7266728691","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8046143882","display_name":null,"funder_award_id":"11PG724N","funder_id":"https://openalex.org/F4320321730","funder_display_name":"Fonds Wetenschappelijk Onderzoek"},{"id":"https://openalex.org/G8055432103","display_name":null,"funder_award_id":"13039/501100011033","funder_id":"https://openalex.org/F4320322930","funder_display_name":"Ministerio de Ciencia e Innovaci\u00f3n"},{"id":"https://openalex.org/G8250324087","display_name":null,"funder_award_id":"PID2020-113082GB-I00","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"},{"id":"https://openalex.org/G8260616629","display_name":null,"funder_award_id":"011033","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320321730","display_name":"Fonds Wetenschappelijk Onderzoek","ror":"https://ror.org/03qtxy027"},{"id":"https://openalex.org/F4320322930","display_name":"Ministerio de Ciencia e Innovaci\u00f3n","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320328447","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4402218236.pdf","grobid_xml":"https://content.openalex.org/works/W4402218236.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1508926025","https://openalex.org/W2046551711","https://openalex.org/W2069711632","https://openalex.org/W2091331782","https://openalex.org/W2092834040","https://openalex.org/W2113797588","https://openalex.org/W2128751442","https://openalex.org/W2140622323","https://openalex.org/W2141424941","https://openalex.org/W2143438504","https://openalex.org/W2162938940","https://openalex.org/W2167413626","https://openalex.org/W2905157741","https://openalex.org/W3041268646","https://openalex.org/W3083164162","https://openalex.org/W6637164687","https://openalex.org/W6638801799","https://openalex.org/W6802490941"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2078468767","https://openalex.org/W4324357120","https://openalex.org/W2185973892","https://openalex.org/W2052643798","https://openalex.org/W2892236424","https://openalex.org/W1977573875","https://openalex.org/W2060804077","https://openalex.org/W2247724920"],"abstract_inverted_index":{"We":[0],"prove":[1,81],"that":[2],"the":[3,82,95],"natural":[4],"isomorphism":[5],"<inline-formula":[6,28,86,100,108],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[7,29,87,101,109],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[8,30,88,102,110],"<tex-math":[9,31,89,103,111],"notation=\"LaTeX\">$\\mathbb":[10],"{F}_{2^{h}}\\cong":[11],"\\mathbb":[12],"{F}":[13],"_{2}^{h}$":[14],"</tex-math></inline-formula>":[15,33,91,105,113],"induces":[16],"a":[17,49,53,60,73,85,99],"bijection":[18],"between":[19],"stabilizer":[20,36,50,70,92,114],"codes":[21,37,47,71],"on":[22,38],"n":[23],"quqits":[24],"with":[25],"local":[26],"dimension":[27],"notation=\"LaTeX\">$q=2^{h}$":[32],"and":[34,94,106],"binary":[35],"hn":[39],"qubits.":[40],"This":[41],"allows":[42],"us":[43],"to":[44,59,80],"describe":[45],"these":[46],"geometrically:":[48],"code":[51,93],"over":[52],"field":[54],"of":[55,64,84,97],"even":[56],"order":[57],"corresponds":[58],"so-called":[61],"quantum":[62],"set":[63],"symplectic":[65],"polar":[66],"spaces.":[67],"Moreover,":[68],"equivalent":[69],"have":[72],"similar":[74],"geometry,":[75],"which":[76],"can":[77],"be":[78],"used":[79],"uniqueness":[83],"notation=\"LaTeX\">$[\\![{4,0,3}]\\!]_{4}$":[90],"nonexistence":[96],"both":[98],"notation=\"LaTeX\">$[\\![{7,1,4}]\\!]_{4}$":[104],"an":[107],"notation=\"LaTeX\">$[\\![{8,0,5}]\\!]_{4}$":[112],"code.":[115]},"counts_by_year":[],"updated_date":"2026-04-07T14:57:38.498316","created_date":"2024-09-05T00:00:00"}
