{"id":"https://openalex.org/W3012885385","doi":"https://doi.org/10.1109/tit.2020.3015681","title":"Non-Split Toric BCH Codes on Singular del Pezzo Surfaces","display_name":"Non-Split Toric BCH Codes on Singular del Pezzo Surfaces","publication_year":2020,"publication_date":"2020-08-11","ids":{"openalex":"https://openalex.org/W3012885385","doi":"https://doi.org/10.1109/tit.2020.3015681","mag":"3012885385"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2020.3015681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.3015681","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/2003.09828","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012748509","display_name":"Dmitrii Koshelev","orcid":"https://orcid.org/0000-0002-4796-8989"},"institutions":[{"id":"https://openalex.org/I195731000","display_name":"Universit\u00e9 de Versailles Saint-Quentin-en-Yvelines","ror":"https://ror.org/03mkjjy25","country_code":"FR","type":"education","lineage":["https://openalex.org/I195731000","https://openalex.org/I277688954"]},{"id":"https://openalex.org/I4210107660","display_name":"Institute for Information Transmission Problems","ror":"https://ror.org/013w2d378","country_code":"RU","type":"facility","lineage":["https://openalex.org/I4210107660"]}],"countries":["FR","RU"],"is_corresponding":true,"raw_author_name":"Dmitrii Koshelev","raw_affiliation_strings":["Algebra and Number Theory Laboratory, Institute for Information Transmission Problems, Moscow, Russia","Center for Research and Advanced Development, Infotecs, Moscow, Russia","Versailles Laboratory of Mathematics, Versailles Saint-Quentin-en-Yvelines University, Versailles, France"],"raw_orcid":"https://orcid.org/0000-0002-4796-8989","affiliations":[{"raw_affiliation_string":"Algebra and Number Theory Laboratory, Institute for Information Transmission Problems, Moscow, Russia","institution_ids":["https://openalex.org/I4210107660"]},{"raw_affiliation_string":"Center for Research and Advanced Development, Infotecs, Moscow, Russia","institution_ids":[]},{"raw_affiliation_string":"Versailles Laboratory of Mathematics, Versailles Saint-Quentin-en-Yvelines University, Versailles, France","institution_ids":["https://openalex.org/I195731000"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012748509"],"corresponding_institution_ids":["https://openalex.org/I195731000","https://openalex.org/I4210107660"],"apc_list":{"value":2045,"currency":"USD","value_usd":2045},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0312159,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"66","issue":"12","first_page":"7341","last_page":"7347"},"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9750000238418579,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T11181","display_name":"Advanced Data Storage Technologies","score":0.9656000137329102,"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/bch-code","display_name":"BCH code","score":0.866661548614502},{"id":"https://openalex.org/keywords/quartic-function","display_name":"Quartic function","score":0.8533384799957275},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7644404172897339},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5142912268638611},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.4701419472694397},{"id":"https://openalex.org/keywords/minimum-distance","display_name":"Minimum distance","score":0.4459533989429474},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4186435341835022},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3610111474990845},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.30556154251098633},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1822739541530609},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.10220366716384888},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.0718831717967987}],"concepts":[{"id":"https://openalex.org/C42276685","wikidata":"https://www.wikidata.org/wiki/Q795705","display_name":"BCH code","level":3,"score":0.866661548614502},{"id":"https://openalex.org/C130432447","wikidata":"https://www.wikidata.org/wiki/Q11420049","display_name":"Quartic function","level":2,"score":0.8533384799957275},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7644404172897339},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5142912268638611},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.4701419472694397},{"id":"https://openalex.org/C3018063660","wikidata":"https://www.wikidata.org/wiki/Q6865448","display_name":"Minimum distance","level":2,"score":0.4459533989429474},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4186435341835022},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3610111474990845},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.30556154251098633},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1822739541530609},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.10220366716384888},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.0718831717967987}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/tit.2020.3015681","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2020.3015681","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:arXiv.org:2003.09828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09828","pdf_url":"https://arxiv.org/pdf/2003.09828","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":"mag:3012885385","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.09828v2","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:HAL:hal-03109144v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03109144","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, 2020, 66 (12), pp.7341-7347. ⟨10.1109/TIT.2020.3015681⟩","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2003.09828","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.09828","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":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2003.09828","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2003.09828","pdf_url":"https://arxiv.org/pdf/2003.09828","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":[],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3012885385.pdf","grobid_xml":"https://content.openalex.org/works/W3012885385.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W1483686281","https://openalex.org/W1486898453","https://openalex.org/W1511314663","https://openalex.org/W1557415002","https://openalex.org/W1574372628","https://openalex.org/W1823587391","https://openalex.org/W1969401961","https://openalex.org/W1999721813","https://openalex.org/W2022788697","https://openalex.org/W2031428201","https://openalex.org/W2054425309","https://openalex.org/W2068153666","https://openalex.org/W2075015671","https://openalex.org/W2098377074","https://openalex.org/W2122825463","https://openalex.org/W2124113125","https://openalex.org/W2134258244","https://openalex.org/W2951379724","https://openalex.org/W2960101832","https://openalex.org/W2963651684","https://openalex.org/W2964302545","https://openalex.org/W3028196707","https://openalex.org/W3102403861","https://openalex.org/W4248269519","https://openalex.org/W4292027090","https://openalex.org/W6642684425"],"related_works":["https://openalex.org/W3015914376","https://openalex.org/W3158543257","https://openalex.org/W2995141891","https://openalex.org/W3210957911","https://openalex.org/W2557775039","https://openalex.org/W2949700705","https://openalex.org/W2781993250","https://openalex.org/W2033521349","https://openalex.org/W3103665618","https://openalex.org/W2953704311","https://openalex.org/W1514322993","https://openalex.org/W3037944244","https://openalex.org/W2269083353","https://openalex.org/W3103816784","https://openalex.org/W2979332709","https://openalex.org/W1442634981","https://openalex.org/W1029223418","https://openalex.org/W2951735389","https://openalex.org/W2897724939","https://openalex.org/W2950067312"],"abstract_inverted_index":{"In":[0,60],"the":[1,56,70,73,76,80,108],"article":[2],"we":[3,16,46,63,105],"construct":[4],"low-rate":[5],"non-split":[6,18],"toric":[7,19],"q-ary":[8],"codes":[9,32,82],"on":[10],"some":[11],"singular":[12,27],"surfaces.":[13],"More":[14],"precisely,":[15],"consider":[17],"cubic":[20],"and":[21],"quartic":[22],"del":[23],"Pezzo":[24],"surfaces,":[25],"whose":[26],"points":[28],"are":[29],"Fq-conjugate.":[30],"Our":[31],"turn":[33],"out":[34],"to":[35,92,101],"be":[36,93],"BCH":[37,67],"ones":[38],"with":[39],"sufficiently":[40],"large":[41],"minimum":[42,58],"distance":[43],"d.":[44],"Indeed,":[45],"prove":[47],"that":[48,100],"d-d*":[49],"\u2265":[50],"q-[2.\u221aq]":[51],"j-1,":[52],"where":[53],"d*":[54],"is":[55,83,97],"designed":[57],"distance.":[59],"other":[61,71],"words,":[62],"significantly":[64],"improve":[65],"upon":[66],"bound.":[68],"On":[69],"hand,":[72],"defect":[74],"of":[75,110],"Griesmer":[77],"bound":[78],"for":[79],"new":[81],"\u2264":[84],"[2.\u221aq]":[85],"j":[86],"-":[87],"1,":[88],"which":[89],"also":[90],"seems":[91],"quite":[94],"good.":[95],"It":[96],"worth":[98],"noting":[99],"better":[102],"estimate":[103],"d":[104],"actively":[106],"use":[107],"theory":[109],"elliptic":[111],"curves":[112],"over":[113],"finite":[114],"fields.":[115]},"counts_by_year":[],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}