{"id":"https://openalex.org/W1973229684","doi":"https://doi.org/10.1109/tit.2014.2361794","title":"Syndrome Generation and Error Location Search for the Decoding of Algebraic-Geometry Codes on Plane Garcia\u2013Stichtenoth Curves","display_name":"Syndrome Generation and Error Location Search for the Decoding of Algebraic-Geometry Codes on Plane Garcia\u2013Stichtenoth Curves","publication_year":2014,"publication_date":"2014-10-08","ids":{"openalex":"https://openalex.org/W1973229684","doi":"https://doi.org/10.1109/tit.2014.2361794","mag":"1973229684"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2014.2361794","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2361794","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":["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/A5110217822","display_name":"Chung-Chin Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Chung-Chin Lu","raw_affiliation_strings":["Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan","Department of Electrical Engineering, National Tsing Hua University Hsinchu, Taiwan#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, National Tsing Hua University, Hsinchu, Taiwan","institution_ids":["https://openalex.org/I25846049"]},{"raw_affiliation_string":"Department of Electrical Engineering, National Tsing Hua University Hsinchu, Taiwan#TAB#","institution_ids":["https://openalex.org/I25846049"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054802758","display_name":"Chih-Yen Yang","orcid":null},"institutions":[{"id":"https://openalex.org/I4880106","display_name":"Feng Chia University","ror":"https://ror.org/05vhczg54","country_code":"TW","type":"education","lineage":["https://openalex.org/I4880106"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chih-Yen Yang","raw_affiliation_strings":["Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Feng Chia University, Taichung, Taiwan","institution_ids":["https://openalex.org/I4880106"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110217822"],"corresponding_institution_ids":["https://openalex.org/I25846049"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05460371,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"60","issue":"12","first_page":"7464","last_page":"7472"},"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/T12162","display_name":"Cellular Automata and Applications","score":0.9940000176429749,"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"}},{"id":"https://openalex.org/T10796","display_name":"Cooperative Communication and Network Coding","score":0.9858999848365784,"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/finite-field","display_name":"Finite field","score":0.6293367147445679},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.6178274750709534},{"id":"https://openalex.org/keywords/algebraic-curve","display_name":"Algebraic curve","score":0.5981111526489258},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4939876198768616},{"id":"https://openalex.org/keywords/plane-curve","display_name":"Plane curve","score":0.4912955164909363},{"id":"https://openalex.org/keywords/garcia","display_name":"Garcia","score":0.47107377648353577},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.47029921412467957},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.46015551686286926},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4585130214691162},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4559384882450104},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.433064341545105},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35967904329299927},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35549038648605347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34441137313842773},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2708818316459656},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18623101711273193}],"concepts":[{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.6293367147445679},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.6178274750709534},{"id":"https://openalex.org/C207043602","wikidata":"https://www.wikidata.org/wiki/Q266237","display_name":"Algebraic curve","level":2,"score":0.5981111526489258},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4939876198768616},{"id":"https://openalex.org/C43809302","wikidata":"https://www.wikidata.org/wiki/Q1060874","display_name":"Plane curve","level":2,"score":0.4912955164909363},{"id":"https://openalex.org/C2776684731","wikidata":"https://www.wikidata.org/wiki/Q5522084","display_name":"Garcia","level":2,"score":0.47107377648353577},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.47029921412467957},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.46015551686286926},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4585130214691162},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4559384882450104},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.433064341545105},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35967904329299927},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35549038648605347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34441137313842773},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2708818316459656},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18623101711273193},{"id":"https://openalex.org/C15708023","wikidata":"https://www.wikidata.org/wiki/Q80083","display_name":"Humanities","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2014.2361794","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2014.2361794","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G892506880","display_name":null,"funder_award_id":"NSC-98-2221-E-007-046-MY3","funder_id":"https://openalex.org/F4320321040","funder_display_name":"National Science Council"}],"funders":[{"id":"https://openalex.org/F4320321040","display_name":"National Science Council","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1534925464","https://openalex.org/W1557415002","https://openalex.org/W1606480398","https://openalex.org/W1996118782","https://openalex.org/W2025536681","https://openalex.org/W2070874501","https://openalex.org/W2097083932","https://openalex.org/W2134732546","https://openalex.org/W2140438256","https://openalex.org/W2159193690","https://openalex.org/W2808892791","https://openalex.org/W6752638544"],"related_works":["https://openalex.org/W2030471012","https://openalex.org/W2051712499","https://openalex.org/W2550122689","https://openalex.org/W1498993739","https://openalex.org/W1647114756","https://openalex.org/W1967787874","https://openalex.org/W4245708675","https://openalex.org/W2139917777","https://openalex.org/W285356538","https://openalex.org/W2167207265"],"abstract_inverted_index":{"In":[0],"this":[1,49],"paper,":[2],"the":[3,42,57,63,69,86],"basic":[4],"function":[5,13],"field":[6],"of":[7,12,23,33,59,65,71],"an":[8],"asymptotically":[9],"optimal":[10],"tower":[11],"fields":[14],"by":[15],"Garcia":[16],"and":[17,62,77],"Stichtenoth":[18],"is":[19,46,53],"studied,":[20],"where":[21],"bases":[22],"one-point":[24],"linear":[25],"systems":[26],"can":[27],"be":[28],"explicitly":[29],"constructed.":[30],"A":[31],"representation":[32,52],"finite":[34],"GF(q":[35],"<sup":[36],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[37],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</sup>":[38],")-rational":[39],"points":[40],"on":[41,85],"associated":[43],"plane":[44,87],"curve":[45],"derived":[47],"in":[48,68],"paper.":[50],"This":[51],"exploited":[54],"to":[55,81],"extend":[56],"use":[58],"Horner's":[60],"loops":[61],"mechanism":[64],"Chien":[66],"search":[67],"decoding":[70],"Reed-Solomon":[72],"codes":[73,83],"for":[74],"syndrome":[75],"generation":[76],"error-location":[78],"search,":[79],"respectively,":[80],"algebraic-geometry":[82],"built":[84],"Garcia-Stichtenoth":[88],"curve.":[89]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}