{"id":"https://openalex.org/W3215246204","doi":"https://doi.org/10.1007/s10623-022-01153-w","title":"On the dimension and structure of the square of the dual of a Goppa code","display_name":"On the dimension and structure of the square of the dual of a Goppa code","publication_year":2022,"publication_date":"2022-11-22","ids":{"openalex":"https://openalex.org/W3215246204","doi":"https://doi.org/10.1007/s10623-022-01153-w","mag":"3215246204"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-022-01153-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-022-01153-w","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://inria.hal.science/hal-03919898","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010936130","display_name":"Rocco Mora","orcid":"https://orcid.org/0000-0001-5165-5320"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210086502","display_name":"CryptoExperts (France)","ror":"https://ror.org/0030xrh72","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210086502"]},{"id":"https://openalex.org/I4210151753","display_name":"Institut Parisien de Chimie Mol\u00e9culaire","ror":"https://ror.org/04qwfwm19","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210128300","https://openalex.org/I4210151753"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Rocco Mora","raw_affiliation_strings":["Sorbonne Universit\u00e9s, UPMC Univ Paris 06, 4 place Jussieu, Paris, 75005, France","Team COSMIQ, Inria, 2 rue Simone Iff, Paris, 75012, France","COSMIQ - Cryptologie syme\u0301trique, cryptologie fonde\u0301e sur les codes et information quantique (2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12  - France)","SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)"],"raw_orcid":"https://orcid.org/0000-0001-5165-5320","affiliations":[{"raw_affiliation_string":"Sorbonne Universit\u00e9s, UPMC Univ Paris 06, 4 place Jussieu, Paris, 75005, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210151753"]},{"raw_affiliation_string":"Team COSMIQ, Inria, 2 rue Simone Iff, Paris, 75012, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"COSMIQ - Cryptologie syme\u0301trique, cryptologie fonde\u0301e sur les codes et information quantique (2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12  - France)","institution_ids":["https://openalex.org/I4210086502"]},{"raw_affiliation_string":"SU - Sorbonne Universite\u0301 (21 rue de l\u2019\u00c9cole de m\u00e9decine - 75006 Paris - France)","institution_ids":["https://openalex.org/I39804081"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060302693","display_name":"Jean\u2013Pierre Tillich","orcid":"https://orcid.org/0000-0002-1709-1792"},"institutions":[{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]},{"id":"https://openalex.org/I4210086502","display_name":"CryptoExperts (France)","ror":"https://ror.org/0030xrh72","country_code":"FR","type":"company","lineage":["https://openalex.org/I4210086502"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Pierre Tillich","raw_affiliation_strings":["Team COSMIQ, Inria, 2 rue Simone Iff, Paris, 75012, France","COSMIQ - Cryptologie syme\u0301trique, cryptologie fonde\u0301e sur les codes et information quantique (2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12  - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Team COSMIQ, Inria, 2 rue Simone Iff, Paris, 75012, France","institution_ids":["https://openalex.org/I1326498283"]},{"raw_affiliation_string":"COSMIQ - Cryptologie syme\u0301trique, cryptologie fonde\u0301e sur les codes et information quantique (2 rue Simone Iff -CS 42112 -75589 Paris Cedex 12  - France)","institution_ids":["https://openalex.org/I4210086502"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5010936130"],"corresponding_institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I39804081","https://openalex.org/I4210086502","https://openalex.org/I4210151753"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":1.022,"has_fulltext":false,"cited_by_count":17,"citation_normalized_percentile":{"value":0.73107126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"91","issue":"4","first_page":"1351","last_page":"1372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},"topics":[{"id":"https://openalex.org/T12029","display_name":"DNA and Biological Computing","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9965999722480774,"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":0.9951000213623047,"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/mathematics","display_name":"Mathematics","score":0.5535941123962402},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5480022430419922},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5407329797744751},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.5231258273124695},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.513282060623169},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4660666286945343},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.4377289116382599},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41871410608291626},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4089423418045044},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30810263752937317},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.25664275884628296},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1980818808078766}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5535941123962402},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5480022430419922},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5407329797744751},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.5231258273124695},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.513282060623169},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4660666286945343},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.4377289116382599},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41871410608291626},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4089423418045044},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30810263752937317},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.25664275884628296},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1980818808078766},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10623-022-01153-w","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10623-022-01153-w","pdf_url":null,"source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03533235v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03533235","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":"2022","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:HAL:hal-03919898v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03919898","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes and Cryptography, 2022, 91 (4), pp.1351--1372. ⟨10.1007/s10623-022-01153-w⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-03919898v1","is_oa":true,"landing_page_url":"https://inria.hal.science/hal-03919898","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Designs, Codes and Cryptography, 2022, 91 (4), pp.1351--1372. ⟨10.1007/s10623-022-01153-w⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2848733872","display_name":"Code-based Cryptography","funder_award_id":"ANR-17-CE39-0007","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G3355261338","display_name":"algeBrA, pRoofs, Algorithms, Curves and sUrfaces for coDes and their Applications","funder_award_id":"ANR-21-CE39-0009","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W31442624","https://openalex.org/W72398006","https://openalex.org/W566315627","https://openalex.org/W1488034582","https://openalex.org/W1510132879","https://openalex.org/W1536493828","https://openalex.org/W1555268962","https://openalex.org/W1575924360","https://openalex.org/W1595415026","https://openalex.org/W1606480398","https://openalex.org/W2015862444","https://openalex.org/W2020484625","https://openalex.org/W2022295314","https://openalex.org/W2065465262","https://openalex.org/W2099250555","https://openalex.org/W2108277687","https://openalex.org/W2111444563","https://openalex.org/W2136772235","https://openalex.org/W2150005435","https://openalex.org/W2304219541","https://openalex.org/W2591819627","https://openalex.org/W2624923838","https://openalex.org/W2950885909","https://openalex.org/W2951541528","https://openalex.org/W3020961574","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2131958170","https://openalex.org/W2061122711","https://openalex.org/W2273754158","https://openalex.org/W4247954915","https://openalex.org/W2336747664","https://openalex.org/W3102623159","https://openalex.org/W2357130048","https://openalex.org/W4206605161","https://openalex.org/W2092234295","https://openalex.org/W1509926844"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":7}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}