{"id":"https://openalex.org/W7212138585","doi":"https://doi.org/10.48550/arxiv.2609.09943","title":"Quantum MDS codes from complements of unions of finite-field subsets","display_name":"Quantum MDS codes from complements of unions of finite-field subsets","publication_year":2026,"publication_date":"2026-09-09","ids":{"openalex":"https://openalex.org/W7212138585","doi":"https://doi.org/10.48550/arxiv.2609.09943"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.09943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09943","pdf_url":"https://arxiv.org/pdf/2609.09943","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,"listed_in":[],"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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.09943","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5140881475","display_name":"Naihong Hu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu, Naihong","raw_affiliation_strings":["School of Mathematical Sciences , MOE Key Laboratory of Mathematics and Engineering Applications & Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai 200241 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , MOE Key Laboratory of Mathematics and Engineering Applications & Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai 200241 , China","institution_ids":["https://openalex.org/I66867065"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101644333","display_name":"Hong Ji","orcid":"https://orcid.org/0000-0003-4896-7213","observed_orcids":["https://orcid.org/0000-0003-4896-7213"]},"institutions":[{"id":"https://openalex.org/I66867065","display_name":"East China Normal University","ror":"https://ror.org/02n96ep67","country_code":"CN","type":"education","lineage":["https://openalex.org/I66867065"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ji, Hong","raw_affiliation_strings":["School of Mathematical Sciences , MOE Key Laboratory of Mathematics and Engineering Applications & Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai 200241 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , MOE Key Laboratory of Mathematics and Engineering Applications & Shanghai Key Laboratory of PMMP , East China Normal University , Shanghai 200241 , China","institution_ids":["https://openalex.org/I66867065"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I66867065"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.0,"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/T11797","display_name":"graph theory and CDMA systems","score":0.0,"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/quantum-mds-codes","display_name":"quantum MDS codes","score":0.9750000238418579},{"id":"https://openalex.org/keywords/hermitian-self-orthogonal-codes","display_name":"Hermitian self-orthogonal codes","score":0.9190000295639038},{"id":"https://openalex.org/keywords/generalized-reed-solomon-codes","display_name":"generalized Reed-Solomon codes","score":0.9990000128746033},{"id":"https://openalex.org/keywords/finite-fields","display_name":"finite fields","score":0.5220000147819519},{"id":"https://openalex.org/keywords/trace-map","display_name":"trace map","score":0.5180000066757202},{"id":"https://openalex.org/keywords/norm-map","display_name":"norm map","score":0.5910000205039978},{"id":"https://openalex.org/keywords/multiplicative-subgroups","display_name":"multiplicative subgroups","score":0.8690000176429749},{"id":"https://openalex.org/keywords/cosets","display_name":"cosets","score":0.6759999990463257},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"minimum distance","score":0.8379999995231628},{"id":"https://openalex.org/keywords/propagation-rules","display_name":"propagation rules","score":0.5569999814033508},{"id":"https://openalex.org/keywords/quantum-error-correcting-codes","display_name":"quantum error-correcting codes","score":0.6620000004768372}],"concepts":[{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.7785999774932861},{"id":"https://openalex.org/C85307737","wikidata":"https://www.wikidata.org/wiki/Q751969","display_name":"Coset","level":2,"score":0.7774999737739563},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7038999795913696},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6434000134468079},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.519599974155426},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.5135999917984009},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4731999933719635},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.428600013256073},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3849000036716461},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.3700999915599823},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.35359999537467957},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.32010000944137573},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.2800000011920929},{"id":"https://openalex.org/C3427991","wikidata":"https://www.wikidata.org/wiki/Q651426","display_name":"Group code","level":5,"score":0.27889999747276306},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.27799999713897705},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.26919999718666077},{"id":"https://openalex.org/C58053490","wikidata":"https://www.wikidata.org/wiki/Q176555","display_name":"Quantum computer","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.26179999113082886},{"id":"https://openalex.org/C2778023678","wikidata":"https://www.wikidata.org/wiki/Q554403","display_name":"Duality (order theory)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.09943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09943","pdf_url":"https://arxiv.org/pdf/2609.09943","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,"listed_in":[],"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":"doi:10.48550/arxiv.2609.09943","doi":"https://doi.org/10.48550/arxiv.2609.09943","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.09943","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.09943","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.09943","pdf_url":"https://arxiv.org/pdf/2609.09943","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,"listed_in":[],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1609915050","display_name":null,"funder_award_id":"22DZ2229014","funder_id":"https://openalex.org/F4320321885","funder_display_name":"Science and Technology Commission of Shanghai Municipality"}],"funders":[{"id":"https://openalex.org/F4320321106","display_name":"Ministry of Education of the People's Republic of China","ror":"https://ror.org/01mv9t934"},{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7212138585.pdf","grobid_xml":"https://content.openalex.org/works/W7212138585.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1471103927","https://openalex.org/W2002370994","https://openalex.org/W2076107177","https://openalex.org/W2112690875","https://openalex.org/W2114207424","https://openalex.org/W2131690084","https://openalex.org/W2143438504","https://openalex.org/W2144634231","https://openalex.org/W2162938940","https://openalex.org/W2167413626","https://openalex.org/W2963998610","https://openalex.org/W2971710266","https://openalex.org/W2991138722","https://openalex.org/W3176234222","https://openalex.org/W3191186496","https://openalex.org/W4309938112","https://openalex.org/W4386156180","https://openalex.org/W4392359651","https://openalex.org/W4400787924","https://openalex.org/W4404222101","https://openalex.org/W4404304557","https://openalex.org/W4411054974","https://openalex.org/W4411077408","https://openalex.org/W4413128160","https://openalex.org/W4413817014","https://openalex.org/W7108083531"],"related_works":["https://openalex.org/W4404222101","https://openalex.org/W3191186496","https://openalex.org/W4321010397","https://openalex.org/W4386156180","https://openalex.org/W7108083531","https://openalex.org/W4322007480","https://openalex.org/W4404304557","https://openalex.org/W7165015260","https://openalex.org/W2002370994","https://openalex.org/W2991138722"],"abstract_inverted_index":{"Let":[0],"$q$":[1],"be":[2],"an":[3],"odd":[4],"prime":[5],"power.":[6],"We":[7,132],"use":[8],"complements":[9],"of":[10,12,14,37,52,68,90,122,143],"unions":[11],"subsets":[13],"$\\mathbb":[15,58],"F_{q^2}$":[16],"as":[17],"locator":[18],"sets":[19,41],"and":[20,40,120],"establish":[21],"a":[22,27],"sufficient":[23],"condition":[24],"under":[25,97],"which":[26,98],"generalized":[28],"Reed--Solomon":[29],"(GRS)":[30],"code":[31],"is":[32],"Hermitian":[33,53,61],"self-orthogonal.":[34],"Using":[35],"cosets":[36,121],"multiplicative":[38,123],"subgroups":[39],"with":[42],"prescribed":[43],"trace":[44,116],"or":[45,127],"norm":[46],"values,":[47],"we":[48,94],"construct":[49],"five":[50,65],"families":[51,67],"self-orthogonal":[54],"GRS":[55],"codes":[56,80,89,100],"over":[57],"F_{q^2}$.":[59],"The":[60],"construction":[62],"then":[63],"yields":[64],"corresponding":[66],"$q$-ary":[69],"quantum":[70,79],"maximum-distance-separable":[71],"(MDS)":[72],"codes.":[73],"Under":[74],"suitable":[75],"parameter":[76],"conditions,":[77],"these":[78],"have":[81,101],"minimum":[82,104],"distances":[83,105],"greater":[84],"than":[85,106],"$q/2+1$.":[86],"By":[87],"comparing":[88],"the":[91,129],"same":[92],"length,":[93],"give":[95],"conditions":[96],"our":[99],"strictly":[102],"larger":[103],"those":[107],"obtainable":[108],"from":[109],"several":[110],"previously":[111],"known":[112],"constructions":[113],"based":[114],"on":[115],"maps,":[117],"linear":[118],"transformations,":[119],"subgroups,":[124],"either":[125],"directly":[126],"via":[128],"propagation":[130],"rule.":[131],"further":[133],"show":[134],"that":[135],"such":[136],"improvements":[137],"occur":[138],"for":[139],"infinitely":[140],"many":[141],"values":[142],"$q$.":[144]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-11T00:00:00"}
