{"id":"https://openalex.org/W1996447801","doi":"https://doi.org/10.1109/isit.2012.6284685","title":"List decoding algorithms based on Gr&amp;#x00F6;bner bases for general one-point AG codes","display_name":"List decoding algorithms based on Gr&amp;#x00F6;bner bases for general one-point AG codes","publication_year":2012,"publication_date":"2012-07-01","ids":{"openalex":"https://openalex.org/W1996447801","doi":"https://doi.org/10.1109/isit.2012.6284685","mag":"1996447801"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2012.6284685","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284685","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1201.6248","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071571524","display_name":"Olav Geil","orcid":"https://orcid.org/0000-0002-9666-3399"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Olav Geil","raw_affiliation_strings":["Department of Mathematical Sciences, University of Aalborg, Denmark","Department of Mathematical Sciences, Aalborg University, Denmark#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Aalborg University, Denmark#TAB#","institution_ids":["https://openalex.org/I891191580"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005174170","display_name":"Ryutaroh Matsumoto","orcid":"https://orcid.org/0000-0002-5085-8879"},"institutions":[{"id":"https://openalex.org/I114531698","display_name":"Tokyo Institute of Technology","ror":"https://ror.org/0112mx960","country_code":"JP","type":"education","lineage":["https://openalex.org/I114531698"]},{"id":"https://openalex.org/I90023481","display_name":"National Institute of Information and Communications Technology","ror":"https://ror.org/016bgq349","country_code":"JP","type":"facility","lineage":["https://openalex.org/I90023481"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Ryutaroh Matsumoto","raw_affiliation_strings":["Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan","Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, 152-8550 Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Communications and Integrated Systems, Tokyo Institute of Technology, Japan","institution_ids":["https://openalex.org/I114531698","https://openalex.org/I90023481"]},{"raw_affiliation_string":"Dept. of Communications and Integrated Systems, Tokyo Institute of Technology, 152-8550 Japan","institution_ids":["https://openalex.org/I114531698"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083432227","display_name":"Diego Ruano","orcid":"https://orcid.org/0000-0001-7304-0087"},"institutions":[{"id":"https://openalex.org/I891191580","display_name":"Aalborg University","ror":"https://ror.org/04m5j1k67","country_code":"DK","type":"education","lineage":["https://openalex.org/I891191580"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"Diego Ruano","raw_affiliation_strings":["Department of Mathematical Sciences, University of Aalborg, Denmark","Department of Mathematical Sciences, Aalborg University, Denmark#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, University of Aalborg, Denmark","institution_ids":["https://openalex.org/I891191580"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Aalborg University, Denmark#TAB#","institution_ids":["https://openalex.org/I891191580"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5601,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.83139283,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"86","last_page":"90"},"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/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":1.0,"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/T10951","display_name":"Cryptographic Implementations and Security","score":0.9868999719619751,"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":0.9704999923706055,"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/decoding-methods","display_name":"Decoding methods","score":0.8447420597076416},{"id":"https://openalex.org/keywords/list-decoding","display_name":"List decoding","score":0.8130568265914917},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6314302682876587},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.6305685043334961},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6189302206039429},{"id":"https://openalex.org/keywords/berlekamp\u2013welch-algorithm","display_name":"Berlekamp\u2013Welch algorithm","score":0.6164310574531555},{"id":"https://openalex.org/keywords/sequential-decoding","display_name":"Sequential decoding","score":0.5932250022888184},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.5746322870254517},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.44477012753486633},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4400154650211334},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3915981650352478},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3475232720375061},{"id":"https://openalex.org/keywords/concatenated-error-correction-code","display_name":"Concatenated error correction code","score":0.3333311080932617},{"id":"https://openalex.org/keywords/block-code","display_name":"Block code","score":0.20434358716011047},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08329951763153076}],"concepts":[{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.8447420597076416},{"id":"https://openalex.org/C204397858","wikidata":"https://www.wikidata.org/wiki/Q4437907","display_name":"List decoding","level":5,"score":0.8130568265914917},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6314302682876587},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.6305685043334961},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6189302206039429},{"id":"https://openalex.org/C132727834","wikidata":"https://www.wikidata.org/wiki/Q4892328","display_name":"Berlekamp\u2013Welch algorithm","level":5,"score":0.6164310574531555},{"id":"https://openalex.org/C193969084","wikidata":"https://www.wikidata.org/wiki/Q7452500","display_name":"Sequential decoding","level":4,"score":0.5932250022888184},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5746322870254517},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44477012753486633},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4400154650211334},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3915981650352478},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3475232720375061},{"id":"https://openalex.org/C78944582","wikidata":"https://www.wikidata.org/wiki/Q5158264","display_name":"Concatenated error correction code","level":4,"score":0.3333311080932617},{"id":"https://openalex.org/C157125643","wikidata":"https://www.wikidata.org/wiki/Q884707","display_name":"Block code","level":3,"score":0.20434358716011047},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08329951763153076},{"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/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/isit.2012.6284685","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2012.6284685","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2012 IEEE International Symposium on Information Theory Proceedings","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1201.6248","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.6248","pdf_url":"https://arxiv.org/pdf/1201.6248","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":"pmh:oai:pure.atira.dk:publications/1a4fe246-e735-4382-ad86-38405d79de64","is_oa":false,"landing_page_url":"https://vbn.aau.dk/da/publications/1a4fe246-e735-4382-ad86-38405d79de64","pdf_url":null,"source":{"id":"https://openalex.org/S4306401731","display_name":"VBN Forskningsportal (Aalborg Universitet)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I891191580","host_organization_name":"Aalborg University","host_organization_lineage":["https://openalex.org/I891191580"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Geil, H O, Matsumoto, R & Ruano, D 2012, List decoding algorithms based on Gr\u00f6bner bases for general one-point AG codes. in Information Theory Proceedings (ISIT) : 2012 IEEE International Symposium on Information Theory. IEEE (Institute of Electrical and Electronics Engineers), Proceedings of the IEEE International Symposium on Information Theory, pp. 86-90, IEEE International Symposium on Information Theory, Cambridge, United States, 01/07/2012. https://doi.org/10.1109/ISIT.2012.6284685","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1201.6248","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1201.6248","pdf_url":"https://arxiv.org/pdf/1201.6248","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1511965816","https://openalex.org/W1557415002","https://openalex.org/W1561016548","https://openalex.org/W1968814246","https://openalex.org/W1976575672","https://openalex.org/W1977024326","https://openalex.org/W1980801869","https://openalex.org/W1990636161","https://openalex.org/W1998899281","https://openalex.org/W2009890571","https://openalex.org/W2016147767","https://openalex.org/W2022968516","https://openalex.org/W2032431003","https://openalex.org/W2034321633","https://openalex.org/W2062823694","https://openalex.org/W2080290915","https://openalex.org/W2086866396","https://openalex.org/W2093877555","https://openalex.org/W2097083932","https://openalex.org/W2097503925","https://openalex.org/W2112639232","https://openalex.org/W2133164811","https://openalex.org/W2143766839","https://openalex.org/W2145830640","https://openalex.org/W2186219138","https://openalex.org/W2479064976","https://openalex.org/W2950993262","https://openalex.org/W2963278054","https://openalex.org/W2963721886","https://openalex.org/W4237780066","https://openalex.org/W4301437154","https://openalex.org/W6686918250"],"related_works":["https://openalex.org/W2385322349","https://openalex.org/W2369600518","https://openalex.org/W2370284973","https://openalex.org/W2028976748","https://openalex.org/W2050784748","https://openalex.org/W2383267581","https://openalex.org/W2102627024","https://openalex.org/W2182594114","https://openalex.org/W2127999627","https://openalex.org/W2010879611"],"abstract_inverted_index":{"We":[0],"generalize":[1,43],"the":[2,38,44,53,74,91,105,121,126],"list":[3,80],"decoding":[4,46,77],"algorithm":[5,47,78],"for":[6,48],"Hermitian":[7],"codes":[8,51],"proposed":[9,56],"by":[10,31,57,110],"Lee":[11],"and":[12,33,60,103,112,124],"O'Sullivan":[13,61],"[15]":[14],"based":[15],"on":[16],"Gr\u00f6bner":[17],"bases":[18],"to":[19,63,79],"general":[20,64],"one-point":[21,49,65],"AG":[22,50,66],"codes,":[23,67],"under":[24],"an":[25],"assumption":[26],"weaker":[27],"than":[28],"one":[29],"used":[30,89],"Beelen":[32],"Brander":[34],"[4].":[35],"By":[36],"using":[37],"same":[39],"principle,":[40],"we":[41,72],"also":[42],"unique":[45,76],"over":[52],"Miura-Kamiya":[54],"Cabcurves":[55],"Lee,":[58],"Bras-Amor\u00f3s":[59],"[14]":[62],"without":[68],"any":[69],"assumption.":[70],"Finally":[71],"extend":[73],"latter":[75],"decoding,":[81],"modify":[82],"it":[83,86,132],"so":[84,130],"that":[85,115,131],"can":[87,133],"be":[88],"with":[90],"Feng-Rao":[92],"improved":[93],"code":[94],"construction,":[95],"prove":[96],"equality":[97],"between":[98],"its":[99],"error":[100],"correcting":[101],"capability":[102],"half":[104],"minimum":[106],"distance":[107],"lower":[108],"bound":[109],"Andersen":[111],"Geil":[113],"[3]":[114],"has":[116],"not":[117],"been":[118],"done":[119],"in":[120],"original":[122],"proposal,":[123],"remove":[125],"unnecessary":[127],"computational":[128],"steps":[129],"run":[134],"faster.":[135]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2016-06-24T00:00:00"}
