{"id":"https://openalex.org/W2512668221","doi":"https://doi.org/10.1109/isit.2016.7541761","title":"A quadratic Welch-Berlekamp algorithm to decode generalized Gabidulin codes, and some variants","display_name":"A quadratic Welch-Berlekamp algorithm to decode generalized Gabidulin codes, and some variants","publication_year":2016,"publication_date":"2016-07-01","ids":{"openalex":"https://openalex.org/W2512668221","doi":"https://doi.org/10.1109/isit.2016.7541761","mag":"2512668221"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2016.7541761","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541761","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-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/A5030702754","display_name":"Gwezheneg Robert","orcid":null},"institutions":[{"id":"https://openalex.org/I4210161663","display_name":"Institut de recherche math\u00e9matique de Rennes","ror":"https://ror.org/05y76vp22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I2800285241","https://openalex.org/I28221208","https://openalex.org/I3124938446","https://openalex.org/I4210117091","https://openalex.org/I4210141950","https://openalex.org/I4210146044","https://openalex.org/I4210161663","https://openalex.org/I4399657933","https://openalex.org/I56067802","https://openalex.org/I56067802"]},{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Gwezheneg Robert","raw_affiliation_strings":["IRMAR, Universit&#x00E9; de Rennes 1, France","IRMAR, Universit\u00e9 de Rennes 1, Rennes, France"],"affiliations":[{"raw_affiliation_string":"IRMAR, Universit&#x00E9; de Rennes 1, France","institution_ids":["https://openalex.org/I4210161663"]},{"raw_affiliation_string":"IRMAR, Universit\u00e9 de Rennes 1, Rennes, France","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I4210161663"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5030702754"],"corresponding_institution_ids":["https://openalex.org/I4210161663","https://openalex.org/I56067802"],"apc_list":null,"apc_paid":null,"fwci":1.7774,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.89460375,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"2559","last_page":"2563"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9998000264167786,"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":0.9998000264167786,"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/T13779","display_name":"Cancer Mechanisms and Therapy","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/2734","display_name":"Pathology and Forensic Medicine"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9860000014305115,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.6748400926589966},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6681371927261353},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.6515235304832458},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6303200721740723},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5800003409385681},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.5458073019981384},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.46306341886520386},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.4221612215042114},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3633057475090027},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.32413721084594727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32279422879219055},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3082398474216461},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.1704806387424469},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.16346383094787598}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.6748400926589966},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6681371927261353},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.6515235304832458},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6303200721740723},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5800003409385681},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.5458073019981384},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.46306341886520386},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.4221612215042114},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3633057475090027},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.32413721084594727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32279422879219055},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3082398474216461},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.1704806387424469},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.16346383094787598},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit.2016.7541761","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2016.7541761","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1871606885","https://openalex.org/W1993359877","https://openalex.org/W1996310087","https://openalex.org/W2014149071","https://openalex.org/W2014449813","https://openalex.org/W2095547380","https://openalex.org/W2114209415","https://openalex.org/W2126824576","https://openalex.org/W2130358229","https://openalex.org/W2331005958","https://openalex.org/W2343763030","https://openalex.org/W3100282565","https://openalex.org/W4236047074","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2385322349","https://openalex.org/W2369600518","https://openalex.org/W2370284973","https://openalex.org/W2357077655","https://openalex.org/W2351361564","https://openalex.org/W2144831582","https://openalex.org/W2129423808","https://openalex.org/W4205451769","https://openalex.org/W1976480044","https://openalex.org/W2488124294"],"abstract_inverted_index":{"Gabidulin":[0],"codes":[1],"are":[2],"Maximum":[3],"Rank":[4],"Distance":[5],"(MRD)":[6],"codes.":[7],"They":[8],"have":[9],"been":[10],"recently":[11],"generalized":[12],"to":[13,24,40],"cyclic":[14],"Galois":[15],"extension":[16],"fields.":[17],"The":[18,29],"unique":[19],"decoding":[20],"problem":[21],"is":[22,34,53,76],"equivalent":[23],"the":[25,35,48,57,71,74],"linear":[26],"reconstruction":[27,43,58],"problem.":[28,44,59],"aim":[30],"of":[31,37,50,56,70],"this":[32,42],"article":[33],"study":[36],"an":[38],"algorithm":[39,52,75],"solve":[41],"We":[45,65],"prove":[46],"that":[47,68],"output":[49],"our":[51],"a":[54],"solution":[55],"Then":[60],"we":[61],"give":[62],"some":[63],"variants.":[64],"also":[66],"establish":[67],"(one":[69],"variant":[72],"of)":[73],"quadratic.":[77]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-03-25T13:04:00.132906","created_date":"2025-10-10T00:00:00"}
