{"id":"https://openalex.org/W4312454786","doi":"https://doi.org/10.1109/tit.2022.3211887","title":"Hulls of Reed-Solomon Codes via Algebraic Geometry Codes","display_name":"Hulls of Reed-Solomon Codes via Algebraic Geometry Codes","publication_year":2022,"publication_date":"2022-10-04","ids":{"openalex":"https://openalex.org/W4312454786","doi":"https://doi.org/10.1109/tit.2022.3211887"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3211887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3211887","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081545653","display_name":"Bocong Chen","orcid":"https://orcid.org/0000-0001-5295-8403"},"institutions":[{"id":"https://openalex.org/I90610280","display_name":"South China University of Technology","ror":"https://ror.org/0530pts50","country_code":"CN","type":"education","lineage":["https://openalex.org/I90610280"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bocong Chen","raw_affiliation_strings":["School of Mathematics, South China University of Technology, Guangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-5295-8403","affiliations":[{"raw_affiliation_string":"School of Mathematics, South China University of Technology, Guangzhou, China","institution_ids":["https://openalex.org/I90610280"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063268716","display_name":"San Ling","orcid":"https://orcid.org/0000-0002-1978-3557"},"institutions":[{"id":"https://openalex.org/I172675005","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302","country_code":"SG","type":"education","lineage":["https://openalex.org/I172675005"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"San Ling","raw_affiliation_strings":["School of Physical and Mathematical Sciences, Nanyang Technological University, Jurong West, Singapore"],"raw_orcid":"https://orcid.org/0000-0002-1978-3557","affiliations":[{"raw_affiliation_string":"School of Physical and Mathematical Sciences, Nanyang Technological University, Jurong West, Singapore","institution_ids":["https://openalex.org/I172675005"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079255508","display_name":"Hongwei Liu","orcid":"https://orcid.org/0000-0003-3503-8220"},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Central China Normal University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0003-3503-8220","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Central China Normal University, Wuhan, China","institution_ids":["https://openalex.org/I40963666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0439,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.80231745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"69","issue":"2","first_page":"1005","last_page":"1014"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998999834060669,"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":0.9998999834060669,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9987000226974487,"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":0.9954000115394592,"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/notation","display_name":"Notation","score":0.6422510147094727},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4677935242652893},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3489956557750702},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34115922451019287},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3264133930206299},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.1969236135482788},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14552199840545654}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6422510147094727},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4677935242652893},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3489956557750702},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34115922451019287},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3264133930206299},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.1969236135482788},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14552199840545654}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3211887","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3211887","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1738987912","display_name":"MDS\u731c\u60f3\u53ca\u76f8\u5173\u95ee\u9898\u7814\u7a76","funder_award_id":"11971175","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5300754835","display_name":null,"funder_award_id":"04INS000047C230GRT01","funder_id":"https://openalex.org/F4320320766","funder_display_name":"Nanyang Technological University"},{"id":"https://openalex.org/G8035838337","display_name":null,"funder_award_id":"12271199","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G93499383","display_name":"\u51e0\u7c7b\u7801\u7684\u7ed3\u6784\u548c\u8ddd\u79bb\u53ca\u5176\u5e94\u7528\u7814\u7a76","funder_award_id":"11871025","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320320766","display_name":"Nanyang Technological University","ror":"https://ror.org/02e7b5302"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1557415002","https://openalex.org/W1976213622","https://openalex.org/W1982432882","https://openalex.org/W1986971697","https://openalex.org/W1999774889","https://openalex.org/W2020636832","https://openalex.org/W2061270859","https://openalex.org/W2063592138","https://openalex.org/W2076748366","https://openalex.org/W2082432729","https://openalex.org/W2109365199","https://openalex.org/W2114207424","https://openalex.org/W2119117325","https://openalex.org/W2284727451","https://openalex.org/W2593067933","https://openalex.org/W2759610897","https://openalex.org/W2897844431","https://openalex.org/W2907627293","https://openalex.org/W2963105100","https://openalex.org/W2963827199","https://openalex.org/W2964293057","https://openalex.org/W2991354072","https://openalex.org/W2997291310","https://openalex.org/W3040174801","https://openalex.org/W3045958266","https://openalex.org/W3092954427","https://openalex.org/W3099628384","https://openalex.org/W3105396280","https://openalex.org/W3121556672","https://openalex.org/W3122350386","https://openalex.org/W3155044924","https://openalex.org/W3180519652","https://openalex.org/W3181644031","https://openalex.org/W3200987404","https://openalex.org/W3202718886","https://openalex.org/W4283317383","https://openalex.org/W6839556185"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2504004674","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Let":[0],"<inline-formula":[1,11,22,31,42,55,67,77,96,117],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[2,12,23,32,43,56,68,78,97,118],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[3,13,24,33,44,57,69,79,98,119],"<tex-math":[4,14,25,34,45,58,70,80,99,120],"notation=\"LaTeX\">${\\mathrm{":[5,71,100],"RS}}_{k}(\\mathbf":[6,72,101,104],"{a})$":[7,73],"</tex-math></inline-formula>":[8,16,28,39,49,60,74,83,107,122],"be":[9,50],"a":[10,51],"notation=\"LaTeX\">$k$":[15],"-dimensional":[17],"Reed-Solomon":[18],"(RS)":[19],"code":[20],"over":[21],"notation=\"LaTeX\">$\\mathbb":[26],"{F}_{q}$":[27],"associated":[29],"with":[30],"notation=\"LaTeX\">$\\mathbf":[35],"{a}=(\\alpha":[36],"_{1},\\cdots,\\alpha":[37],"_{n})$":[38],"and":[40,123,144],"let":[41],"notation=\"LaTeX\">$h=\\prod":[46],"_{i=1}^{n}(z-\\alpha":[47],"_{i})$":[48],"polynomial":[52],"in":[53,108],"variable":[54],"notation=\"LaTeX\">$z$":[59],".":[61],"In":[62],"this":[63],"paper,":[64],"by":[65],"expressing":[66],"as":[75],"an":[76],"notation=\"LaTeX\">$\\mathcal":[81],"{L}$":[82],"-construction":[84],"algebraic":[85],"geometry":[86],"code,":[87],"we":[88,129],"completely":[89],"determine":[90,131],"the":[91,94,111,114,132],"dimension":[92],"of":[93,110,113,116,134],"hull":[95],"{a})\\bigcap":[102],"{\\mathrm{":[103],"{a})^{\\perp}":[105],"$":[106],"terms":[109],"degree":[112],"derivative":[115],"notation=\"LaTeX\">$h$":[121],"some":[124],"relevant":[125],"polynomials.":[126],"As":[127],"applications,":[128],"explicitly":[130],"parameters":[133],"MDS":[135],"entanglement-assisted":[136],"quantum":[137],"error-correcting":[138],"codes":[139,152],"constructed":[140],"from":[141],"RS":[142,151],"codes,":[143],"all":[145],"linear":[146],"complementary":[147],"dual":[148],"(resp.":[149],"self-dual)":[150],"are":[153],"also":[154],"fully":[155],"described.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}