{"id":"https://openalex.org/W4221156773","doi":"https://doi.org/10.1007/978-3-031-15979-4_18","title":"On\u00a0Codes\u00a0and\u00a0Learning\u00a0with\u00a0Errors\u00a0over Function Fields","display_name":"On\u00a0Codes\u00a0and\u00a0Learning\u00a0with\u00a0Errors\u00a0over Function Fields","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4221156773","doi":"https://doi.org/10.1007/978-3-031-15979-4_18"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-031-15979-4_18","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-15979-4_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2202.13990","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038074457","display_name":"Maxime Bombar","orcid":"https://orcid.org/0000-0001-9081-6094"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Maxime Bombar","raw_affiliation_strings":["Inria Saclay, Palaiseau, France","LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, 91120, Palaiseau Cedex, France","LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d'Estienne d'Orves, 91120, Palaiseau Cedex, France"],"raw_orcid":"https://orcid.org/0000-0001-9081-6094","affiliations":[{"raw_affiliation_string":"Inria Saclay, Palaiseau, France","institution_ids":["https://openalex.org/I4210126360"]},{"raw_affiliation_string":"LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, 91120, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d'Estienne d'Orves, 91120, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063131196","display_name":"Alain Couvreur","orcid":"https://orcid.org/0000-0003-4554-6720"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alain Couvreur","raw_affiliation_strings":["Inria Saclay, Palaiseau, France","LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, 91120, Palaiseau Cedex, France","LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d'Estienne d'Orves, 91120, Palaiseau Cedex, France"],"raw_orcid":"https://orcid.org/0000-0003-4554-6720","affiliations":[{"raw_affiliation_string":"Inria Saclay, Palaiseau, France","institution_ids":["https://openalex.org/I4210126360"]},{"raw_affiliation_string":"LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, 91120, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d'Estienne d'Orves, 91120, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083024466","display_name":"Thomas Debris-Alazard","orcid":"https://orcid.org/0000-0001-8864-0245"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210126360","display_name":"Centre Inria de Saclay","ror":"https://ror.org/0315e5x55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1326498283","https://openalex.org/I4210126360"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Thomas Debris-Alazard","raw_affiliation_strings":["Inria Saclay, Palaiseau, France","LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, 91120, Palaiseau Cedex, France","LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d'Estienne d'Orves, 91120, Palaiseau Cedex, France"],"raw_orcid":"https://orcid.org/0000-0001-8864-0245","affiliations":[{"raw_affiliation_string":"Inria Saclay, Palaiseau, France","institution_ids":["https://openalex.org/I4210126360"]},{"raw_affiliation_string":"LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d\u2019Estienne d\u2019Orves, 91120, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"LIX, CNRS UMR 7161, \u00c9cole Polytechnique, Institut Polytechnique de Paris, 1 rue Honor\u00e9 d'Estienne d'Orves, 91120, Palaiseau Cedex, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038074457"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I4210126360"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.7118,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.85812081,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"513","last_page":"540"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","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/T10237","display_name":"Cryptography and Data Security","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/T11130","display_name":"Coding theory and cryptography","score":0.9997000098228455,"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/T11567","display_name":"semigroups and automata theory","score":0.9972000122070312,"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/learning-with-errors","display_name":"Learning with errors","score":0.7412298917770386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6711675524711609},{"id":"https://openalex.org/keywords/cryptography","display_name":"Cryptography","score":0.6291738152503967},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5884286761283875},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5260087251663208},{"id":"https://openalex.org/keywords/polynomial-ring","display_name":"Polynomial ring","score":0.4909239411354065},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.48463043570518494},{"id":"https://openalex.org/keywords/linear-code","display_name":"Linear code","score":0.41278672218322754},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.3511413335800171},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3494206666946411},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3449501097202301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3009309768676758},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.28503796458244324},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.25357407331466675}],"concepts":[{"id":"https://openalex.org/C2779014939","wikidata":"https://www.wikidata.org/wiki/Q6510239","display_name":"Learning with errors","level":3,"score":0.7412298917770386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6711675524711609},{"id":"https://openalex.org/C178489894","wikidata":"https://www.wikidata.org/wiki/Q8789","display_name":"Cryptography","level":2,"score":0.6291738152503967},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5884286761283875},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5260087251663208},{"id":"https://openalex.org/C9485509","wikidata":"https://www.wikidata.org/wiki/Q1455652","display_name":"Polynomial ring","level":3,"score":0.4909239411354065},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.48463043570518494},{"id":"https://openalex.org/C2400350","wikidata":"https://www.wikidata.org/wiki/Q1752667","display_name":"Linear code","level":4,"score":0.41278672218322754},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.3511413335800171},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3494206666946411},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3449501097202301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3009309768676758},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.28503796458244324},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.25357407331466675},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-031-15979-4_18","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-031-15979-4_18","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},{"id":"pmh:oai:arXiv.org:2202.13990","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.13990","pdf_url":"https://arxiv.org/pdf/2202.13990","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-03597834v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03597834","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":"CRYPTO 2022, Aug 2022, Santa Barbara (CA), United States. pp.513-540, &#x27E8;10.1007/978-3-031-15979-4_18&#x27E9;","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2202.13990","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.13990","pdf_url":"https://arxiv.org/pdf/2202.13990","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},"sustainable_development_goals":[{"score":0.7900000214576721,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W15967873","https://openalex.org/W49599189","https://openalex.org/W1491861813","https://openalex.org/W1527005907","https://openalex.org/W1537715321","https://openalex.org/W1557415002","https://openalex.org/W1595415026","https://openalex.org/W1857557921","https://openalex.org/W1872498068","https://openalex.org/W1961257075","https://openalex.org/W1965275036","https://openalex.org/W1970323954","https://openalex.org/W1985439922","https://openalex.org/W2003177806","https://openalex.org/W2057642197","https://openalex.org/W2061949491","https://openalex.org/W2077244027","https://openalex.org/W2094249908","https://openalex.org/W2098290658","https://openalex.org/W2105882027","https://openalex.org/W2114664664","https://openalex.org/W2171001107","https://openalex.org/W2171084480","https://openalex.org/W2479064976","https://openalex.org/W2619674633","https://openalex.org/W2626019822","https://openalex.org/W2774174285","https://openalex.org/W2795036470","https://openalex.org/W2798359482","https://openalex.org/W2913851998","https://openalex.org/W2985767532","https://openalex.org/W2989843281","https://openalex.org/W2990439290","https://openalex.org/W3048468015","https://openalex.org/W3082330489","https://openalex.org/W3170034244","https://openalex.org/W3214801537","https://openalex.org/W4241310425","https://openalex.org/W4249844765","https://openalex.org/W4254706618"],"related_works":["https://openalex.org/W4300994926","https://openalex.org/W2035028562","https://openalex.org/W2550942574","https://openalex.org/W2315723423","https://openalex.org/W2964302506","https://openalex.org/W3029426427","https://openalex.org/W2397608281","https://openalex.org/W2179033149","https://openalex.org/W3203968505","https://openalex.org/W2899523861"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
