{"id":"https://openalex.org/W2165107287","doi":"https://doi.org/10.1109/18.382034","title":"Error-locator ideals for algebraic-geometric codes","display_name":"Error-locator ideals for algebraic-geometric codes","publication_year":1995,"publication_date":"1995-05-01","ids":{"openalex":"https://openalex.org/W2165107287","doi":"https://doi.org/10.1109/18.382034","mag":"2165107287"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/18.382034","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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/A5108532168","display_name":"D.A. Leonard","orcid":null},"institutions":[],"countries":["US"],"is_corresponding":true,"raw_author_name":"D.A. Leonard","raw_affiliation_strings":["Department of Discrete and Statistical Sciences Math Annex, Aubum University, Auburn, AL, USA"],"affiliations":[{"raw_affiliation_string":"Department of Discrete and Statistical Sciences Math Annex, Aubum University, Auburn, AL, USA","institution_ids":[]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5108532168"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.111,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":9,"citation_normalized_percentile":{"value":0.746802,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":76,"max":77},"biblio":{"volume":"41","issue":"3","first_page":"819","last_page":"824"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9999,"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":0.9999,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.987,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.9798,"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/code","display_name":"Code (set theory)","score":0.43686604}],"concepts":[{"id":"https://openalex.org/C2776639384","wikidata":"https://www.wikidata.org/wiki/Q840396","display_name":"Ideal (ethics)","level":2,"score":0.6874198},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.63547474},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5638644},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5412116},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5215951},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.49703434},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.49474213},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.48693216},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44495502},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.43686604},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.43324792},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.32617944},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30095178},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13515025},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11510867},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07891825},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"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},{"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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1109/18.382034","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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":16,"referenced_works":["https://openalex.org/W1536231005","https://openalex.org/W1578250293","https://openalex.org/W1607153847","https://openalex.org/W1635749692","https://openalex.org/W2064810618","https://openalex.org/W2097083932","https://openalex.org/W2104379151","https://openalex.org/W2127579297","https://openalex.org/W2131723039","https://openalex.org/W2141839400","https://openalex.org/W2162442687","https://openalex.org/W2165471216","https://openalex.org/W2165855190","https://openalex.org/W2334439626","https://openalex.org/W2985767532","https://openalex.org/W3144798926"],"related_works":["https://openalex.org/W4302615923","https://openalex.org/W4220731478","https://openalex.org/W3203142394","https://openalex.org/W2590472383","https://openalex.org/W2393580911","https://openalex.org/W2383873009","https://openalex.org/W2351061015","https://openalex.org/W2212184297","https://openalex.org/W2017509870","https://openalex.org/W1974101135"],"abstract_inverted_index":{"The":[0,27,123],"error":[1,75],"locations":[2],"for":[3,39,49],"an":[4,52],"algebraic-geometric":[5,41],"code":[6],"C*(D,mP)":[7],"are":[8,125],"exactly":[9,129],"the":[10,35,89,94,121,130,137],"common":[11,131],"zeros":[12,132],"(that":[13],"is,":[14],"a":[15,20,30,46,111,116],"projective":[16],"variety":[17],"V(I))":[18],"of":[19,24,34,54,67,76,93,120,133,136],"set":[21,48],"(ideal)":[22],"I":[23,50],"error-locator":[25,138],"functions.":[26],"paper":[28],"gives":[29],"one-dimensional":[31],"Berlekamp-Massey":[32],"version":[33],"Feng-Rao":[36],"(1993)":[37],"algorithm":[38,97],"decoding":[40],"codes":[42],"C*(D,mP).":[43],"This":[44,96],"produces":[45],"generating":[47],"(as":[51],"ideal)":[53],"size":[55],"at":[56,65,78,99],"most":[57,79,100],"/spl":[58,82,86],"rho/":[59],"(the":[60],"smallest":[61],"positive":[62],"pole":[63],"order":[64],"P":[66],"any":[68,74],"function":[69,119],"in":[70],"L(mP))":[71],"relative":[72],"to":[73],"weight":[77],"e<":[80],"1/2":[81],"delta//sub":[83,87],"m/*,":[84],"with":[85,109],"m/*:=m-2g+2":[88],"designed":[90],"minimum":[91],"distance":[92],"code.":[95],"requires":[98],"c(/spl":[101],"rho/m/sup":[102],"2/+N/spl":[103],"rho/m+/spl":[104],"rho//sup":[105],"2/m)":[106],"field":[107],"multiplications,":[108],"c":[110],"small":[112,117],"constant,":[113],"and":[114],"N":[115],"constant":[118],"curve.":[122],"error-positions":[124],"then":[126],"given":[127],"as":[128],"generator":[134],"functions":[135],"ideal":[139],"I.<":[140],">":[143]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2165107287","counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2024-12-10T01:27:15.060813","created_date":"2016-06-24"}